A condition for scattered linearized polynomials involving Dickson matrices

Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Zanella, Corrado [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Linear set Linearized polynomial -Polynomial Finite projective line Scattered linear set Dickson matrix

Anmerkung:	© Springer Nature Switzerland AG 2019

Übergeordnetes Werk:	Enthalten in: Journal of geometry - Cham : Springer International Publishing AG, 1971, 110(2019), 3 vom: 23. Sept.
Übergeordnetes Werk:	volume:110 ; year:2019 ; number:3 ; day:23 ; month:09

Links:	Volltext

DOI / URN:	10.1007/s00022-019-0505-z

Katalog-ID:	SPR000209511

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245	1	2	\|a A condition for scattered linearized polynomials involving Dickson matrices
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520			\|a Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve.
650		4	\|a Linear set \|7 (dpeaa)DE-He213
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650		4	\|a Finite projective line \|7 (dpeaa)DE-He213
650		4	\|a Scattered linear set \|7 (dpeaa)DE-He213
650		4	\|a Dickson matrix \|7 (dpeaa)DE-He213
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912			\|a GBV_USEFLAG_A
912			\|a SYSFLAG_A
912			\|a GBV_SPRINGER
912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4277
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
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Indexfelder

author_variant	c z cz
matchkey_str	article:14208997:2019----::cniinosatrdierzdoyoilivl
hierarchy_sort_str	2019
publishDate	2019
allfields	10.1007/s00022-019-0505-z doi (DE-627)SPR000209511 (SPR)s00022-019-0505-z-e DE-627 ger DE-627 rakwb eng Zanella, Corrado verfasserin (orcid)0000-0002-5031-1961 aut A condition for scattered linearized polynomials involving Dickson matrices 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2019 Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. Linear set (dpeaa)DE-He213 Linearized polynomial (dpeaa)DE-He213 -Polynomial (dpeaa)DE-He213 Finite projective line (dpeaa)DE-He213 Scattered linear set (dpeaa)DE-He213 Dickson matrix (dpeaa)DE-He213 Enthalten in Journal of geometry Cham : Springer International Publishing AG, 1971 110(2019), 3 vom: 23. Sept. (DE-627)329555944 (DE-600)2047712-0 1420-8997 nnns volume:110 year:2019 number:3 day:23 month:09 https://dx.doi.org/10.1007/s00022-019-0505-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2019 3 23 09
spelling	10.1007/s00022-019-0505-z doi (DE-627)SPR000209511 (SPR)s00022-019-0505-z-e DE-627 ger DE-627 rakwb eng Zanella, Corrado verfasserin (orcid)0000-0002-5031-1961 aut A condition for scattered linearized polynomials involving Dickson matrices 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2019 Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. Linear set (dpeaa)DE-He213 Linearized polynomial (dpeaa)DE-He213 -Polynomial (dpeaa)DE-He213 Finite projective line (dpeaa)DE-He213 Scattered linear set (dpeaa)DE-He213 Dickson matrix (dpeaa)DE-He213 Enthalten in Journal of geometry Cham : Springer International Publishing AG, 1971 110(2019), 3 vom: 23. Sept. (DE-627)329555944 (DE-600)2047712-0 1420-8997 nnns volume:110 year:2019 number:3 day:23 month:09 https://dx.doi.org/10.1007/s00022-019-0505-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2019 3 23 09
allfields_unstemmed	10.1007/s00022-019-0505-z doi (DE-627)SPR000209511 (SPR)s00022-019-0505-z-e DE-627 ger DE-627 rakwb eng Zanella, Corrado verfasserin (orcid)0000-0002-5031-1961 aut A condition for scattered linearized polynomials involving Dickson matrices 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2019 Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. Linear set (dpeaa)DE-He213 Linearized polynomial (dpeaa)DE-He213 -Polynomial (dpeaa)DE-He213 Finite projective line (dpeaa)DE-He213 Scattered linear set (dpeaa)DE-He213 Dickson matrix (dpeaa)DE-He213 Enthalten in Journal of geometry Cham : Springer International Publishing AG, 1971 110(2019), 3 vom: 23. Sept. (DE-627)329555944 (DE-600)2047712-0 1420-8997 nnns volume:110 year:2019 number:3 day:23 month:09 https://dx.doi.org/10.1007/s00022-019-0505-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2019 3 23 09
allfieldsGer	10.1007/s00022-019-0505-z doi (DE-627)SPR000209511 (SPR)s00022-019-0505-z-e DE-627 ger DE-627 rakwb eng Zanella, Corrado verfasserin (orcid)0000-0002-5031-1961 aut A condition for scattered linearized polynomials involving Dickson matrices 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2019 Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. Linear set (dpeaa)DE-He213 Linearized polynomial (dpeaa)DE-He213 -Polynomial (dpeaa)DE-He213 Finite projective line (dpeaa)DE-He213 Scattered linear set (dpeaa)DE-He213 Dickson matrix (dpeaa)DE-He213 Enthalten in Journal of geometry Cham : Springer International Publishing AG, 1971 110(2019), 3 vom: 23. Sept. (DE-627)329555944 (DE-600)2047712-0 1420-8997 nnns volume:110 year:2019 number:3 day:23 month:09 https://dx.doi.org/10.1007/s00022-019-0505-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2019 3 23 09
allfieldsSound	10.1007/s00022-019-0505-z doi (DE-627)SPR000209511 (SPR)s00022-019-0505-z-e DE-627 ger DE-627 rakwb eng Zanella, Corrado verfasserin (orcid)0000-0002-5031-1961 aut A condition for scattered linearized polynomials involving Dickson matrices 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2019 Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. Linear set (dpeaa)DE-He213 Linearized polynomial (dpeaa)DE-He213 -Polynomial (dpeaa)DE-He213 Finite projective line (dpeaa)DE-He213 Scattered linear set (dpeaa)DE-He213 Dickson matrix (dpeaa)DE-He213 Enthalten in Journal of geometry Cham : Springer International Publishing AG, 1971 110(2019), 3 vom: 23. Sept. (DE-627)329555944 (DE-600)2047712-0 1420-8997 nnns volume:110 year:2019 number:3 day:23 month:09 https://dx.doi.org/10.1007/s00022-019-0505-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2019 3 23 09
language	English
source	Enthalten in Journal of geometry 110(2019), 3 vom: 23. Sept. volume:110 year:2019 number:3 day:23 month:09
sourceStr	Enthalten in Journal of geometry 110(2019), 3 vom: 23. Sept. volume:110 year:2019 number:3 day:23 month:09
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Linear set Linearized polynomial -Polynomial Finite projective line Scattered linear set Dickson matrix
isfreeaccess_bool	false
container_title	Journal of geometry
authorswithroles_txt_mv	Zanella, Corrado @@aut@@
publishDateDaySort_date	2019-09-23T00:00:00Z
hierarchy_top_id	329555944
id	SPR000209511
language_de	englisch
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General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. 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author	Zanella, Corrado
spellingShingle	Zanella, Corrado misc Linear set misc Linearized polynomial misc -Polynomial misc Finite projective line misc Scattered linear set misc Dickson matrix A condition for scattered linearized polynomials involving Dickson matrices
authorStr	Zanella, Corrado
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topic_title	A condition for scattered linearized polynomials involving Dickson matrices Linear set (dpeaa)DE-He213 Linearized polynomial (dpeaa)DE-He213 -Polynomial (dpeaa)DE-He213 Finite projective line (dpeaa)DE-He213 Scattered linear set (dpeaa)DE-He213 Dickson matrix (dpeaa)DE-He213
topic	misc Linear set misc Linearized polynomial misc -Polynomial misc Finite projective line misc Scattered linear set misc Dickson matrix
topic_unstemmed	misc Linear set misc Linearized polynomial misc -Polynomial misc Finite projective line misc Scattered linear set misc Dickson matrix
topic_browse	misc Linear set misc Linearized polynomial misc -Polynomial misc Finite projective line misc Scattered linear set misc Dickson matrix
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	A condition for scattered linearized polynomials involving Dickson matrices
ctrlnum	(DE-627)SPR000209511 (SPR)s00022-019-0505-z-e
title_full	A condition for scattered linearized polynomials involving Dickson matrices
author_sort	Zanella, Corrado
journal	Journal of geometry
journalStr	Journal of geometry
lang_code	eng
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author_browse	Zanella, Corrado
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author-letter	Zanella, Corrado
doi_str_mv	10.1007/s00022-019-0505-z
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title_sort	condition for scattered linearized polynomials involving dickson matrices
title_auth	A condition for scattered linearized polynomials involving Dickson matrices
abstract	Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. © Springer Nature Switzerland AG 2019
abstractGer	Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. © Springer Nature Switzerland AG 2019
abstract_unstemmed	Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve. © Springer Nature Switzerland AG 2019
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title_short	A condition for scattered linearized polynomials involving Dickson matrices
url	https://dx.doi.org/10.1007/s00022-019-0505-z
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doi_str	10.1007/s00022-019-0505-z
up_date	2024-07-03T14:39:44.003Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR000209511</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327141906.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2019 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00022-019-0505-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR000209511</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00022-019-0505-z-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zanella, Corrado</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-5031-1961</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A condition for scattered linearized polynomials involving Dickson matrices</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Nature Switzerland AG 2019</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A linearized polynomial over %${{\mathbb {F}}}_{q^n}%$ is called scattered when for any %$t,x\in {{\mathbb {F}}}_{q^n}%$, the condition %$xf(t)-tf(x)=0%$ holds if and only if x and t are %${\mathbb {F}}_q%$-linearly dependent. General conditions for linearized polynomials over %${{\mathbb {F}}}_{q^n}%$ to be scattered can be deduced from the recent results in Csajbók (Scalar q-subresultants and Dickson matrices, 2018), Csajbók et al. (Finite Fields Appl 56:109–130, 2019), McGuire and Sheekey (Finite Fields Appl 57:68–91, 2019), Polverino and Zullo (On the number of roots of some linearized polynomials, 2019). Some of them are based on the Dickson matrix associated with a linearized polynomial. Here a new condition involving Dickson matrices is stated. This condition is then applied to the Lunardon–Polverino binomial %$x^{q^s}+\delta x^{q^{n-s}}%$, allowing to prove that for any n and s, if %${{\,\mathrm{N}\,}}_{q^n/q}(\delta )=1%$, then the binomial is not scattered. Also, a necessary and sufficient condition for %$x^{q^s}+bx^{q^{2s}}%$ to be scattered is shown which is stated in terms of a special plane algebraic curve.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear set</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linearized polynomial</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-Polynomial</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finite projective line</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scattered linear set</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dickson matrix</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of geometry</subfield><subfield code="d">Cham : Springer International Publishing AG, 1971</subfield><subfield code="g">110(2019), 3 vom: 23. 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A condition for scattered linearized polynomials involving Dickson matrices

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