On the kernel of Z2^s-linear Hadamard codes

Mercè Villanueva; Cristina Fernández-Córdoba; Carlos Vela

doi:10.1007/978-3-319-66278-7_10

On the kernel of Z2^s-linear Hadamard codes

Mercè Villanueva, Cristina Fernández-Córdoba, Carlos Vela^*

^*Autor corresponent d’aquest treball

Universitat Autònoma de Barcelona (UAB)

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Resum

The Z_2s-additive codes are subgroups of Z_2s ⁿ, and can be seen as a generalization of linear codes over Z₂ and Z₄. A Z_2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z_2s -additive code. For s=2, the kernel of Z₄ -linear Hadamard codes can be used for their complete classification. In this paper, the kernel of Z_2s -linear Hadamard codes is given for s > 2. However, unlike for s=2, we show that the dimension of the kernel just allows a partial classification of these Hadamard codes.

Idioma original	Anglès
Pàgines (de-a)	107-117
Nombre de pàgines	11
Revista	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
DOIs	https://doi.org/10.1007/978-3-319-66278-7_10
Estat de la publicació	Publicada - 2017

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10.1007/978-3-319-66278-7_10

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@article{aa2e2049617f43b8851c5212ccdf6662,

title = "On the kernel of Z2\textasciicircum{}s-linear Hadamard codes",

abstract = "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. For s=2, the kernel of Z4 -linear Hadamard codes can be used for their complete classification. In this paper, the kernel of Z2s -linear Hadamard codes is given for s > 2. However, unlike for s=2, we show that the dimension of the kernel just allows a partial classification of these Hadamard codes.",

keywords = "Hadamard code, Gray map, Classification, Z-additive code, Kernel, Z-linear code",

author = "Merc{\`e} Villanueva and Cristina Fern{\'a}ndez-C{\'o}rdoba and Carlos Vela",

note = "Funding Information: This work has been partially supported by the Spanish MINECO under Grants TIN2016-77918-P (AEI/FEDER, UE) and MTM2015-69138-REDT, and by the Catalan AGAUR under Grant 2014SGR-691. Publisher Copyright: {\textcopyright} 2017, Springer International Publishing AG. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",

year = "2017",

doi = "10.1007/978-3-319-66278-7\_10",

language = "English",

pages = "107--117",

journal = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

issn = "0302-9743",

publisher = "Springer Science and Business Media Deutschland GmbH",

}

TY - JOUR

T1 - On the kernel of Z2^s-linear Hadamard codes

AU - Villanueva, Mercè

AU - Fernández-Córdoba, Cristina

AU - Vela, Carlos

N1 - Funding Information: This work has been partially supported by the Spanish MINECO under Grants TIN2016-77918-P (AEI/FEDER, UE) and MTM2015-69138-REDT, and by the Catalan AGAUR under Grant 2014SGR-691. Publisher Copyright: © 2017, Springer International Publishing AG. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

N2 - 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. For s=2, the kernel of Z4 -linear Hadamard codes can be used for their complete classification. In this paper, the kernel of Z2s -linear Hadamard codes is given for s > 2. However, unlike for s=2, we show that the dimension of the kernel just allows a partial classification of these Hadamard codes.

AB - 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. For s=2, the kernel of Z4 -linear Hadamard codes can be used for their complete classification. In this paper, the kernel of Z2s -linear Hadamard codes is given for s > 2. However, unlike for s=2, we show that the dimension of the kernel just allows a partial classification of these Hadamard codes.

KW - Hadamard code

KW - Gray map

KW - Classification

KW - Z-additive code

KW - Kernel

KW - Z-linear code

UR - https://dialnet.unirioja.es/servlet/articulo?codigo=8708688

UR - https://www.scopus.com/pages/publications/85028549729

U2 - 10.1007/978-3-319-66278-7_10

DO - 10.1007/978-3-319-66278-7_10

M3 - Article

AN - SCOPUS:85028549729

SN - 0302-9743

SP - 107

EP - 117

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -

On the kernel of Z2^s-linear Hadamard codes

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