Equivalences among Z2s -linear Hadamard codes

The Z2s -additive codes are subgroups of Z2s n, and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s -additive code. A partial classification of these codes by using the dimension of the kernel...

Full description

Bibliographic Details
Authors: Fernández Córdoba, Cristina|||0000-0001-5880-144X, Vela, Carlos|||0000-0003-3362-8817, Villanueva, M|||0000-0001-6179-0833
Format: article
Publication Date:2020
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:239897
Online Access:https://ddd.uab.cat/record/239897
https://dx.doi.org/urn:doi:10.1016/j.disc.2019.111721
Access Level:Open access
Keyword:Classification
Gray map
Hadamard code
Kernel
Rank
Z-additive code
Theoretical Computer Science
Discrete Mathematics and Combinatorics
id ES_5f5dd2a75dc9f5ce9f012ee7f4c5afb3
oai_identifier_str oai:ddd.uab.cat:239897
network_acronym_str ES
network_name_str España
repository_id_str
spelling Equivalences among Z2s -linear Hadamard codesFernández Córdoba, Cristina|||0000-0001-5880-144XVela, Carlos|||0000-0003-3362-8817Villanueva, M|||0000-0001-6179-0833ClassificationGray mapHadamard codeKernelRankZ-additive codeTheoretical Computer ScienceDiscrete Mathematics and CombinatoricsThe Z2s -additive codes are subgroups of Z2s n, and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s -additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some Z2s -linear Hadamard codes of length 2t are equivalent, once t is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to t=11, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on s∈{2,3}, the full classification of the Z2s -linear Hadamard codes of length 2t is established by giving the exact number of such codes. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501SMURhttp://purl.org/coar/version/c_71e4c1898caa6e32info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/239897https://dx.doi.org/urn:doi:10.1016/j.disc.2019.111721reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 TIN2016-77918-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-00463open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2398972026-06-06T12:50:31Z
dc.title.none.fl_str_mv Equivalences among Z2s -linear Hadamard codes
title Equivalences among Z2s -linear Hadamard codes
spellingShingle Equivalences among Z2s -linear Hadamard codes
Fernández Córdoba, Cristina|||0000-0001-5880-144X
Classification
Gray map
Hadamard code
Kernel
Rank
Z-additive code
Theoretical Computer Science
Discrete Mathematics and Combinatorics
title_short Equivalences among Z2s -linear Hadamard codes
title_full Equivalences among Z2s -linear Hadamard codes
title_fullStr Equivalences among Z2s -linear Hadamard codes
title_full_unstemmed Equivalences among Z2s -linear Hadamard codes
title_sort Equivalences among Z2s -linear Hadamard codes
dc.creator.none.fl_str_mv Fernández Córdoba, Cristina|||0000-0001-5880-144X
Vela, Carlos|||0000-0003-3362-8817
Villanueva, M|||0000-0001-6179-0833
author Fernández Córdoba, Cristina|||0000-0001-5880-144X
author_facet Fernández Córdoba, Cristina|||0000-0001-5880-144X
Vela, Carlos|||0000-0003-3362-8817
Villanueva, M|||0000-0001-6179-0833
author_role author
author2 Vela, Carlos|||0000-0003-3362-8817
Villanueva, M|||0000-0001-6179-0833
author2_role author
author
dc.subject.none.fl_str_mv Classification
Gray map
Hadamard code
Kernel
Rank
Z-additive code
Theoretical Computer Science
Discrete Mathematics and Combinatorics
topic Classification
Gray map
Hadamard code
Kernel
Rank
Z-additive code
Theoretical Computer Science
Discrete Mathematics and Combinatorics
description The Z2s -additive codes are subgroups of Z2s n, and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s -additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some Z2s -linear Hadamard codes of length 2t are equivalent, once t is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to t=11, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on s∈{2,3}, the full classification of the Z2s -linear Hadamard codes of length 2t is established by giving the exact number of such codes.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
SMUR
http://purl.org/coar/version/c_71e4c1898caa6e32
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/239897
https://dx.doi.org/urn:doi:10.1016/j.disc.2019.111721
url https://ddd.uab.cat/record/239897
https://dx.doi.org/urn:doi:10.1016/j.disc.2019.111721
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 TIN2016-77918-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-00463
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/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
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869409201035411457
score 15,300719

Similar Items