More permutation polynomials with Niho exponents which permute

Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Cao, Xiwang [verfasserIn] Hou, Xiang-Dong [verfasserIn] Mi, Jiafu [verfasserIn] Xu, Shanding [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Permutation polynomial Trinomial Niho exponent Finite field

Übergeordnetes Werk:	Enthalten in: No title available - 62
Übergeordnetes Werk:	volume:62

DOI / URN:	10.1016/j.ffa.2019.101626

Katalog-ID:	ELV003496910

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allfields	10.1016/j.ffa.2019.101626 doi (DE-627)ELV003496910 (ELSEVIER)S1071-5797(19)30129-7 DE-627 ger DE-627 rda eng Cao, Xiwang verfasserin aut More permutation polynomials with Niho exponents which permute 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. Permutation polynomial Trinomial Niho exponent Finite field Hou, Xiang-Dong verfasserin aut Mi, Jiafu verfasserin aut Xu, Shanding verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_65 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 62
spelling	10.1016/j.ffa.2019.101626 doi (DE-627)ELV003496910 (ELSEVIER)S1071-5797(19)30129-7 DE-627 ger DE-627 rda eng Cao, Xiwang verfasserin aut More permutation polynomials with Niho exponents which permute 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. Permutation polynomial Trinomial Niho exponent Finite field Hou, Xiang-Dong verfasserin aut Mi, Jiafu verfasserin aut Xu, Shanding verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_65 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 62
allfields_unstemmed	10.1016/j.ffa.2019.101626 doi (DE-627)ELV003496910 (ELSEVIER)S1071-5797(19)30129-7 DE-627 ger DE-627 rda eng Cao, Xiwang verfasserin aut More permutation polynomials with Niho exponents which permute 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. Permutation polynomial Trinomial Niho exponent Finite field Hou, Xiang-Dong verfasserin aut Mi, Jiafu verfasserin aut Xu, Shanding verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_65 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 62
allfieldsGer	10.1016/j.ffa.2019.101626 doi (DE-627)ELV003496910 (ELSEVIER)S1071-5797(19)30129-7 DE-627 ger DE-627 rda eng Cao, Xiwang verfasserin aut More permutation polynomials with Niho exponents which permute 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. Permutation polynomial Trinomial Niho exponent Finite field Hou, Xiang-Dong verfasserin aut Mi, Jiafu verfasserin aut Xu, Shanding verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_65 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 62
allfieldsSound	10.1016/j.ffa.2019.101626 doi (DE-627)ELV003496910 (ELSEVIER)S1071-5797(19)30129-7 DE-627 ger DE-627 rda eng Cao, Xiwang verfasserin aut More permutation polynomials with Niho exponents which permute 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. Permutation polynomial Trinomial Niho exponent Finite field Hou, Xiang-Dong verfasserin aut Mi, Jiafu verfasserin aut Xu, Shanding verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_65 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 62
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author	Cao, Xiwang
spellingShingle	Cao, Xiwang misc Permutation polynomial misc Trinomial misc Niho exponent misc Finite field More permutation polynomials with Niho exponents which permute
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topic_title	More permutation polynomials with Niho exponents which permute Permutation polynomial Trinomial Niho exponent Finite field
topic	misc Permutation polynomial misc Trinomial misc Niho exponent misc Finite field
topic_unstemmed	misc Permutation polynomial misc Trinomial misc Niho exponent misc Finite field
topic_browse	misc Permutation polynomial misc Trinomial misc Niho exponent misc Finite field
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	More permutation polynomials with Niho exponents which permute
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title_full	More permutation polynomials with Niho exponents which permute
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author_browse	Cao, Xiwang Hou, Xiang-Dong Mi, Jiafu Xu, Shanding
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author-letter	Cao, Xiwang
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title_sort	more permutation polynomials with niho exponents which permute
title_auth	More permutation polynomials with Niho exponents which permute
abstract	Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials.
abstractGer	Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials.
abstract_unstemmed	Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials.
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title_short	More permutation polynomials with Niho exponents which permute
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author2	Hou, Xiang-Dong Mi, Jiafu Xu, Shanding
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doi_str	10.1016/j.ffa.2019.101626
up_date	2024-07-06T19:49:16.792Z
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In this paper, we construct several classes of permutation trinomials over F p 2 k with Niho exponents of the form f ( x ) = x + λ 1 x s ( p k − 1 ) + 1 + λ 2 x t ( p k − 1 ) + 1 ; some necessary and sufficient conditions for the polynomial f ( x ) to permute F p 2 k are provided. Specifically, for p = 5 , new permutation trinomials are presented. 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score	7.4013004

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