Some classes of complete permutation polynomials over $\mathbb{F}_q $

Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient a...
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Autor*in:	Wu, GaoFei [verfasserIn] Li, Nian [verfasserIn] Helleseth, Tor [verfasserIn] Zhang, YuQing [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	finite field complete permutation polynomials Walsh transform Niho exponents Dickson polynomials

Übergeordnetes Werk:	Enthalten in: Science in China - Asheville, NC : Science in China Press, 1995, 58(2015), 10 vom: 05. Jan., Seite 1-14
Übergeordnetes Werk:	volume:58 ; year:2015 ; number:10 ; day:05 ; month:01 ; pages:1-14

Links:	Volltext

DOI / URN:	10.1007/s11425-014-4964-2

Katalog-ID:	SPR019140320

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520			\|a Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.
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allfields	10.1007/s11425-014-4964-2 doi (DE-627)SPR019140320 (SPR)s11425-014-4964-2-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Wu, GaoFei verfasserin aut Some classes of complete permutation polynomials over $\mathbb{F}_q $ 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work. finite field (dpeaa)DE-He213 complete permutation polynomials (dpeaa)DE-He213 Walsh transform (dpeaa)DE-He213 Niho exponents (dpeaa)DE-He213 Dickson polynomials (dpeaa)DE-He213 Li, Nian verfasserin aut Helleseth, Tor verfasserin aut Zhang, YuQing verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 58(2015), 10 vom: 05. Jan., Seite 1-14 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:58 year:2015 number:10 day:05 month:01 pages:1-14 https://dx.doi.org/10.1007/s11425-014-4964-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE 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_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_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 58 2015 10 05 01 1-14
spelling	10.1007/s11425-014-4964-2 doi (DE-627)SPR019140320 (SPR)s11425-014-4964-2-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Wu, GaoFei verfasserin aut Some classes of complete permutation polynomials over $\mathbb{F}_q $ 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work. finite field (dpeaa)DE-He213 complete permutation polynomials (dpeaa)DE-He213 Walsh transform (dpeaa)DE-He213 Niho exponents (dpeaa)DE-He213 Dickson polynomials (dpeaa)DE-He213 Li, Nian verfasserin aut Helleseth, Tor verfasserin aut Zhang, YuQing verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 58(2015), 10 vom: 05. Jan., Seite 1-14 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:58 year:2015 number:10 day:05 month:01 pages:1-14 https://dx.doi.org/10.1007/s11425-014-4964-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE 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_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_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 58 2015 10 05 01 1-14
allfields_unstemmed	10.1007/s11425-014-4964-2 doi (DE-627)SPR019140320 (SPR)s11425-014-4964-2-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Wu, GaoFei verfasserin aut Some classes of complete permutation polynomials over $\mathbb{F}_q $ 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work. finite field (dpeaa)DE-He213 complete permutation polynomials (dpeaa)DE-He213 Walsh transform (dpeaa)DE-He213 Niho exponents (dpeaa)DE-He213 Dickson polynomials (dpeaa)DE-He213 Li, Nian verfasserin aut Helleseth, Tor verfasserin aut Zhang, YuQing verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 58(2015), 10 vom: 05. Jan., Seite 1-14 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:58 year:2015 number:10 day:05 month:01 pages:1-14 https://dx.doi.org/10.1007/s11425-014-4964-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE 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_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_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 58 2015 10 05 01 1-14
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allfieldsSound	10.1007/s11425-014-4964-2 doi (DE-627)SPR019140320 (SPR)s11425-014-4964-2-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Wu, GaoFei verfasserin aut Some classes of complete permutation polynomials over $\mathbb{F}_q $ 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work. finite field (dpeaa)DE-He213 complete permutation polynomials (dpeaa)DE-He213 Walsh transform (dpeaa)DE-He213 Niho exponents (dpeaa)DE-He213 Dickson polynomials (dpeaa)DE-He213 Li, Nian verfasserin aut Helleseth, Tor verfasserin aut Zhang, YuQing verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 58(2015), 10 vom: 05. Jan., Seite 1-14 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:58 year:2015 number:10 day:05 month:01 pages:1-14 https://dx.doi.org/10.1007/s11425-014-4964-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE 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_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_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 58 2015 10 05 01 1-14
language	English
source	Enthalten in Science in China 58(2015), 10 vom: 05. Jan., Seite 1-14 volume:58 year:2015 number:10 day:05 month:01 pages:1-14
sourceStr	Enthalten in Science in China 58(2015), 10 vom: 05. Jan., Seite 1-14 volume:58 year:2015 number:10 day:05 month:01 pages:1-14
format_phy_str_mv	Article
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topic_facet	finite field complete permutation polynomials Walsh transform Niho exponents Dickson polynomials
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authorswithroles_txt_mv	Wu, GaoFei @@aut@@ Li, Nian @@aut@@ Helleseth, Tor @@aut@@ Zhang, YuQing @@aut@@
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author	Wu, GaoFei
spellingShingle	Wu, GaoFei ddc 510 bkl 30.00 bkl 31.00 misc finite field misc complete permutation polynomials misc Walsh transform misc Niho exponents misc Dickson polynomials Some classes of complete permutation polynomials over $\mathbb{F}_q $
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topic_title	510 530 520 ASE 30.00 bkl 31.00 bkl Some classes of complete permutation polynomials over $\mathbb{F}_q $ finite field (dpeaa)DE-He213 complete permutation polynomials (dpeaa)DE-He213 Walsh transform (dpeaa)DE-He213 Niho exponents (dpeaa)DE-He213 Dickson polynomials (dpeaa)DE-He213
topic	ddc 510 bkl 30.00 bkl 31.00 misc finite field misc complete permutation polynomials misc Walsh transform misc Niho exponents misc Dickson polynomials
topic_unstemmed	ddc 510 bkl 30.00 bkl 31.00 misc finite field misc complete permutation polynomials misc Walsh transform misc Niho exponents misc Dickson polynomials
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title	Some classes of complete permutation polynomials over $\mathbb{F}_q $
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title_full	Some classes of complete permutation polynomials over $\mathbb{F}_q $
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title_sort	some classes of complete permutation polynomials over $\mathbb{f}_q $
title_auth	Some classes of complete permutation polynomials over $\mathbb{F}_q $
abstract	Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.
abstractGer	Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.
abstract_unstemmed	Abstract By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a−1xd to be a complete permutation polynomial over $\mathbb{F}_{p^{4k} } $, where \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$d = \frac{{p^{4k} - 1}}{{p^k - 1}} + 1$\end{document} and $a \in \mathbb{F}_{p^{4k} }^* $. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.
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title_short	Some classes of complete permutation polynomials over $\mathbb{F}_q $
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