On a class of binomial bent functions over the finite fields of odd characteristic

Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the be...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Zheng, Dabin [verfasserIn] Yu, Long Hu, Lei

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	-ary bent function Regular bent function Exponential sum

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2013

Übergeordnetes Werk:	Enthalten in: Applicable algebra in engineering, communication and computing - Berlin : Springer, 1990, 24(2013), 6 vom: 07. Aug., Seite 461-475
Übergeordnetes Werk:	volume:24 ; year:2013 ; number:6 ; day:07 ; month:08 ; pages:461-475

Links:	Volltext

DOI / URN:	10.1007/s00200-013-0202-3

Katalog-ID:	SPR001757768

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245	1	0	\|a On a class of binomial bent functions over the finite fields of odd characteristic
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520			\|a Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones.
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650		4	\|a Regular bent function \|7 (dpeaa)DE-He213
650		4	\|a Exponential sum \|7 (dpeaa)DE-He213
700	1		\|a Yu, Long \|4 aut
700	1		\|a Hu, Lei \|4 aut
773	0	8	\|i Enthalten in \|t Applicable algebra in engineering, communication and computing \|d Berlin : Springer, 1990 \|g 24(2013), 6 vom: 07. Aug., Seite 461-475 \|w (DE-627)253389909 \|w (DE-600)1458434-7 \|x 1432-0622 \|7 nnns
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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_101
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_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_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_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_4012
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
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912			\|a GBV_ILN_4242
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912			\|a GBV_ILN_4249
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912			\|a GBV_ILN_4334
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912			\|a GBV_ILN_4336
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publishDate	2013
allfields	10.1007/s00200-013-0202-3 doi (DE-627)SPR001757768 (SPR)s00200-013-0202-3-e DE-627 ger DE-627 rakwb eng Zheng, Dabin verfasserin aut On a class of binomial bent functions over the finite fields of odd characteristic 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. -ary bent function (dpeaa)DE-He213 Regular bent function (dpeaa)DE-He213 Exponential sum (dpeaa)DE-He213 Yu, Long aut Hu, Lei aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 24(2013), 6 vom: 07. Aug., Seite 461-475 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:24 year:2013 number:6 day:07 month:08 pages:461-475 https://dx.doi.org/10.1007/s00200-013-0202-3 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_101 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_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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2013 6 07 08 461-475
spelling	10.1007/s00200-013-0202-3 doi (DE-627)SPR001757768 (SPR)s00200-013-0202-3-e DE-627 ger DE-627 rakwb eng Zheng, Dabin verfasserin aut On a class of binomial bent functions over the finite fields of odd characteristic 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. -ary bent function (dpeaa)DE-He213 Regular bent function (dpeaa)DE-He213 Exponential sum (dpeaa)DE-He213 Yu, Long aut Hu, Lei aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 24(2013), 6 vom: 07. Aug., Seite 461-475 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:24 year:2013 number:6 day:07 month:08 pages:461-475 https://dx.doi.org/10.1007/s00200-013-0202-3 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_101 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_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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2013 6 07 08 461-475
allfields_unstemmed	10.1007/s00200-013-0202-3 doi (DE-627)SPR001757768 (SPR)s00200-013-0202-3-e DE-627 ger DE-627 rakwb eng Zheng, Dabin verfasserin aut On a class of binomial bent functions over the finite fields of odd characteristic 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. -ary bent function (dpeaa)DE-He213 Regular bent function (dpeaa)DE-He213 Exponential sum (dpeaa)DE-He213 Yu, Long aut Hu, Lei aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 24(2013), 6 vom: 07. Aug., Seite 461-475 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:24 year:2013 number:6 day:07 month:08 pages:461-475 https://dx.doi.org/10.1007/s00200-013-0202-3 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_101 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_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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2013 6 07 08 461-475
allfieldsGer	10.1007/s00200-013-0202-3 doi (DE-627)SPR001757768 (SPR)s00200-013-0202-3-e DE-627 ger DE-627 rakwb eng Zheng, Dabin verfasserin aut On a class of binomial bent functions over the finite fields of odd characteristic 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. -ary bent function (dpeaa)DE-He213 Regular bent function (dpeaa)DE-He213 Exponential sum (dpeaa)DE-He213 Yu, Long aut Hu, Lei aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 24(2013), 6 vom: 07. Aug., Seite 461-475 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:24 year:2013 number:6 day:07 month:08 pages:461-475 https://dx.doi.org/10.1007/s00200-013-0202-3 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_101 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_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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2013 6 07 08 461-475
allfieldsSound	10.1007/s00200-013-0202-3 doi (DE-627)SPR001757768 (SPR)s00200-013-0202-3-e DE-627 ger DE-627 rakwb eng Zheng, Dabin verfasserin aut On a class of binomial bent functions over the finite fields of odd characteristic 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. -ary bent function (dpeaa)DE-He213 Regular bent function (dpeaa)DE-He213 Exponential sum (dpeaa)DE-He213 Yu, Long aut Hu, Lei aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 24(2013), 6 vom: 07. Aug., Seite 461-475 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:24 year:2013 number:6 day:07 month:08 pages:461-475 https://dx.doi.org/10.1007/s00200-013-0202-3 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_101 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_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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2013 6 07 08 461-475
language	English
source	Enthalten in Applicable algebra in engineering, communication and computing 24(2013), 6 vom: 07. Aug., Seite 461-475 volume:24 year:2013 number:6 day:07 month:08 pages:461-475
sourceStr	Enthalten in Applicable algebra in engineering, communication and computing 24(2013), 6 vom: 07. Aug., Seite 461-475 volume:24 year:2013 number:6 day:07 month:08 pages:461-475
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	-ary bent function Regular bent function Exponential sum
isfreeaccess_bool	false
container_title	Applicable algebra in engineering, communication and computing
authorswithroles_txt_mv	Zheng, Dabin @@aut@@ Yu, Long @@aut@@ Hu, Lei @@aut@@
publishDateDaySort_date	2013-08-07T00:00:00Z
hierarchy_top_id	253389909
id	SPR001757768
language_de	englisch
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author	Zheng, Dabin
spellingShingle	Zheng, Dabin misc -ary bent function misc Regular bent function misc Exponential sum On a class of binomial bent functions over the finite fields of odd characteristic
authorStr	Zheng, Dabin
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topic_title	On a class of binomial bent functions over the finite fields of odd characteristic -ary bent function (dpeaa)DE-He213 Regular bent function (dpeaa)DE-He213 Exponential sum (dpeaa)DE-He213
topic	misc -ary bent function misc Regular bent function misc Exponential sum
topic_unstemmed	misc -ary bent function misc Regular bent function misc Exponential sum
topic_browse	misc -ary bent function misc Regular bent function misc Exponential sum
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title	On a class of binomial bent functions over the finite fields of odd characteristic
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title_full	On a class of binomial bent functions over the finite fields of odd characteristic
author_sort	Zheng, Dabin
journal	Applicable algebra in engineering, communication and computing
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author_browse	Zheng, Dabin Yu, Long Hu, Lei
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author-letter	Zheng, Dabin
doi_str_mv	10.1007/s00200-013-0202-3
title_sort	on a class of binomial bent functions over the finite fields of odd characteristic
title_auth	On a class of binomial bent functions over the finite fields of odd characteristic
abstract	Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. © Springer-Verlag Berlin Heidelberg 2013
abstractGer	Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. © Springer-Verlag Berlin Heidelberg 2013
abstract_unstemmed	Abstract We give a necessary and sufficient condition such that the class of %$p%$-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case %$\gcd (\frac{t}{2}, p^{\frac{n}{2}}+1)=1%$ for some even integers %$t%$ and %$n%$. Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones. © Springer-Verlag Berlin Heidelberg 2013
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title_short	On a class of binomial bent functions over the finite fields of odd characteristic
url	https://dx.doi.org/10.1007/s00200-013-0202-3
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up_date	2024-07-04T00:16:18.185Z
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On a class of binomial bent functions over the finite fields of odd characteristic

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