Two infinite classes of rotation symmetric bent functions with simple representation
Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Tang, Chunming [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
Rotation symmetric bent functions |
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| Anmerkung: |
© Springer-Verlag GmbH Germany 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Applicable algebra in engineering, communication and computing - Berlin : Springer, 1990, 29(2017), 3 vom: 18. Aug., Seite 197-208 |
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| Übergeordnetes Werk: |
volume:29 ; year:2017 ; number:3 ; day:18 ; month:08 ; pages:197-208 |
| Links: |
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| DOI / URN: |
10.1007/s00200-017-0337-8 |
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| Katalog-ID: |
SPR001759167 |
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| 520 | |a Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. | ||
| 650 | 4 | |a Bent functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Rotation symmetric bent functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a The Maiorana–McFarland class of bent functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Algebraic degree |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Qi, Yanfeng |4 aut | |
| 700 | 1 | |a Zhou, Zhengchun |4 aut | |
| 700 | 1 | |a Fan, Cuiling |4 aut | |
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10.1007/s00200-017-0337-8 doi (DE-627)SPR001759167 (SPR)s00200-017-0337-8-e DE-627 ger DE-627 rakwb eng Tang, Chunming verfasserin aut Two infinite classes of rotation symmetric bent functions with simple representation 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany 2017 Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. Bent functions (dpeaa)DE-He213 Rotation symmetric bent functions (dpeaa)DE-He213 The Maiorana–McFarland class of bent functions (dpeaa)DE-He213 Algebraic degree (dpeaa)DE-He213 Qi, Yanfeng aut Zhou, Zhengchun aut Fan, Cuiling aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 29(2017), 3 vom: 18. Aug., Seite 197-208 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:29 year:2017 number:3 day:18 month:08 pages:197-208 https://dx.doi.org/10.1007/s00200-017-0337-8 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 29 2017 3 18 08 197-208 |
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10.1007/s00200-017-0337-8 doi (DE-627)SPR001759167 (SPR)s00200-017-0337-8-e DE-627 ger DE-627 rakwb eng Tang, Chunming verfasserin aut Two infinite classes of rotation symmetric bent functions with simple representation 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany 2017 Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. Bent functions (dpeaa)DE-He213 Rotation symmetric bent functions (dpeaa)DE-He213 The Maiorana–McFarland class of bent functions (dpeaa)DE-He213 Algebraic degree (dpeaa)DE-He213 Qi, Yanfeng aut Zhou, Zhengchun aut Fan, Cuiling aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 29(2017), 3 vom: 18. Aug., Seite 197-208 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:29 year:2017 number:3 day:18 month:08 pages:197-208 https://dx.doi.org/10.1007/s00200-017-0337-8 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 29 2017 3 18 08 197-208 |
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10.1007/s00200-017-0337-8 doi (DE-627)SPR001759167 (SPR)s00200-017-0337-8-e DE-627 ger DE-627 rakwb eng Tang, Chunming verfasserin aut Two infinite classes of rotation symmetric bent functions with simple representation 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany 2017 Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. Bent functions (dpeaa)DE-He213 Rotation symmetric bent functions (dpeaa)DE-He213 The Maiorana–McFarland class of bent functions (dpeaa)DE-He213 Algebraic degree (dpeaa)DE-He213 Qi, Yanfeng aut Zhou, Zhengchun aut Fan, Cuiling aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 29(2017), 3 vom: 18. Aug., Seite 197-208 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:29 year:2017 number:3 day:18 month:08 pages:197-208 https://dx.doi.org/10.1007/s00200-017-0337-8 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 29 2017 3 18 08 197-208 |
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10.1007/s00200-017-0337-8 doi (DE-627)SPR001759167 (SPR)s00200-017-0337-8-e DE-627 ger DE-627 rakwb eng Tang, Chunming verfasserin aut Two infinite classes of rotation symmetric bent functions with simple representation 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany 2017 Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. Bent functions (dpeaa)DE-He213 Rotation symmetric bent functions (dpeaa)DE-He213 The Maiorana–McFarland class of bent functions (dpeaa)DE-He213 Algebraic degree (dpeaa)DE-He213 Qi, Yanfeng aut Zhou, Zhengchun aut Fan, Cuiling aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 29(2017), 3 vom: 18. Aug., Seite 197-208 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:29 year:2017 number:3 day:18 month:08 pages:197-208 https://dx.doi.org/10.1007/s00200-017-0337-8 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 29 2017 3 18 08 197-208 |
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10.1007/s00200-017-0337-8 doi (DE-627)SPR001759167 (SPR)s00200-017-0337-8-e DE-627 ger DE-627 rakwb eng Tang, Chunming verfasserin aut Two infinite classes of rotation symmetric bent functions with simple representation 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany 2017 Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. Bent functions (dpeaa)DE-He213 Rotation symmetric bent functions (dpeaa)DE-He213 The Maiorana–McFarland class of bent functions (dpeaa)DE-He213 Algebraic degree (dpeaa)DE-He213 Qi, Yanfeng aut Zhou, Zhengchun aut Fan, Cuiling aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 29(2017), 3 vom: 18. Aug., Seite 197-208 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:29 year:2017 number:3 day:18 month:08 pages:197-208 https://dx.doi.org/10.1007/s00200-017-0337-8 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 29 2017 3 18 08 197-208 |
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Enthalten in Applicable algebra in engineering, communication and computing 29(2017), 3 vom: 18. Aug., Seite 197-208 volume:29 year:2017 number:3 day:18 month:08 pages:197-208 |
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Enthalten in Applicable algebra in engineering, communication and computing 29(2017), 3 vom: 18. Aug., Seite 197-208 volume:29 year:2017 number:3 day:18 month:08 pages:197-208 |
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Bent functions Rotation symmetric bent functions The Maiorana–McFarland class of bent functions Algebraic degree |
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Applicable algebra in engineering, communication and computing |
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Tang, Chunming @@aut@@ Qi, Yanfeng @@aut@@ Zhou, Zhengchun @@aut@@ Fan, Cuiling @@aut@@ |
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In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bent functions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rotation symmetric bent functions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">The Maiorana–McFarland class of bent functions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic degree</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Qi, Yanfeng</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhou, Zhengchun</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fan, Cuiling</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Applicable algebra in engineering, communication and computing</subfield><subfield code="d">Berlin : Springer, 1990</subfield><subfield code="g">29(2017), 3 vom: 18. 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Tang, Chunming |
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Tang, Chunming misc Bent functions misc Rotation symmetric bent functions misc The Maiorana–McFarland class of bent functions misc Algebraic degree Two infinite classes of rotation symmetric bent functions with simple representation |
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Two infinite classes of rotation symmetric bent functions with simple representation Bent functions (dpeaa)DE-He213 Rotation symmetric bent functions (dpeaa)DE-He213 The Maiorana–McFarland class of bent functions (dpeaa)DE-He213 Algebraic degree (dpeaa)DE-He213 |
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misc Bent functions misc Rotation symmetric bent functions misc The Maiorana–McFarland class of bent functions misc Algebraic degree |
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Two infinite classes of rotation symmetric bent functions with simple representation |
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two infinite classes of rotation symmetric bent functions with simple representation |
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Two infinite classes of rotation symmetric bent functions with simple representation |
| abstract |
Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. © Springer-Verlag GmbH Germany 2017 |
| abstractGer |
Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. © Springer-Verlag GmbH Germany 2017 |
| abstract_unstemmed |
Abstract In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on %${\mathbb {F}}_2^{n}%$ of the two forms:f(x)=∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f(x)=\sum _{i=0}^{m-1}x_ix_{i+m} + {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$,ft(x)=∑i=0n-1(xixi+txi+m+xixi+t)+∑i=0m-1xixi+m+γ(x0+xm,…,xm-1+x2m-1)%$f_t(x)= \sum _{i=0}^{n-1}(x_ix_{i+t}x_{i+m} +x_{i}x_{i+t})+ \sum _{i=0}^{m-1}x_ix_{i+m}+ {\gamma }(x_0+x_m,\ldots , x_{m-1}+x_{2m-1})%$, where %$n=2m%$, %${\gamma }(X_0,X_1,\ldots , X_{m-1})%$ is any rotation symmetric polynomial, and %$m/\textit{gcd}(m,t)%$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint. © Springer-Verlag GmbH Germany 2017 |
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| title_short |
Two infinite classes of rotation symmetric bent functions with simple representation |
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https://dx.doi.org/10.1007/s00200-017-0337-8 |
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Qi, Yanfeng Zhou, Zhengchun Fan, Cuiling |
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Qi, Yanfeng Zhou, Zhengchun Fan, Cuiling |
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| doi_str |
10.1007/s00200-017-0337-8 |
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2024-07-04T00:16:38.467Z |
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| score |
7.401144 |