Permutation and local permutation polynomials of maximum degree

Let Fq be the finite field with q elements and Fq [x1, . . . , xn] the ring of polynomials in n variables over Fq . In this paper we consider permutation polynomials and local permutation polynomials over Fq [x1, . . . , xn], which define interesting generalizations of permutations over finite field...

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Detalles Bibliográficos
Autores: Gutiérrez Gutiérrez, Jaime, Jiménez Urroz, Jorge
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/35837
Acceso en línea:https://hdl.handle.net/10902/35837
Access Level:acceso abierto
Palabra clave:Permutation polynomial
Dickson polynomial
Local permutation polynomials
Finite Fields
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spelling Permutation and local permutation polynomials of maximum degreeGutiérrez Gutiérrez, JaimeJiménez Urroz, JorgePermutation polynomialDickson polynomialLocal permutation polynomialsFinite FieldsLet Fq be the finite field with q elements and Fq [x1, . . . , xn] the ring of polynomials in n variables over Fq . In this paper we consider permutation polynomials and local permutation polynomials over Fq [x1, . . . , xn], which define interesting generalizations of permutations over finite fields. We are able to construct permutation polynomials in Fq [x1, . . . , xn] of maximum degree n(q - 1) -1 and local permutation polynomials in Fq [x1, . . . , xn] of maximum degree n(q - 2) when q > 3, extending previous resultsOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureSpringerUniversidad de Cantabria20252025-03-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/35837Afrika Matematika, 2025, 36(1), 45reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/358372026-06-02T12:39:31Z
dc.title.none.fl_str_mv Permutation and local permutation polynomials of maximum degree
title Permutation and local permutation polynomials of maximum degree
spellingShingle Permutation and local permutation polynomials of maximum degree
Gutiérrez Gutiérrez, Jaime
Permutation polynomial
Dickson polynomial
Local permutation polynomials
Finite Fields
title_short Permutation and local permutation polynomials of maximum degree
title_full Permutation and local permutation polynomials of maximum degree
title_fullStr Permutation and local permutation polynomials of maximum degree
title_full_unstemmed Permutation and local permutation polynomials of maximum degree
title_sort Permutation and local permutation polynomials of maximum degree
dc.creator.none.fl_str_mv Gutiérrez Gutiérrez, Jaime
Jiménez Urroz, Jorge
author Gutiérrez Gutiérrez, Jaime
author_facet Gutiérrez Gutiérrez, Jaime
Jiménez Urroz, Jorge
author_role author
author2 Jiménez Urroz, Jorge
author2_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Permutation polynomial
Dickson polynomial
Local permutation polynomials
Finite Fields
topic Permutation polynomial
Dickson polynomial
Local permutation polynomials
Finite Fields
description Let Fq be the finite field with q elements and Fq [x1, . . . , xn] the ring of polynomials in n variables over Fq . In this paper we consider permutation polynomials and local permutation polynomials over Fq [x1, . . . , xn], which define interesting generalizations of permutations over finite fields. We are able to construct permutation polynomials in Fq [x1, . . . , xn] of maximum degree n(q - 1) -1 and local permutation polynomials in Fq [x1, . . . , xn] of maximum degree n(q - 2) when q > 3, extending previous results
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/35837
url https://hdl.handle.net/10902/35837
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Afrika Matematika, 2025, 36(1), 45
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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