On the kernel of Z2s-linear hadamard codes

Cristina Fernández-Córdoba; Carlos Vela; Mercè Villanueva

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

On the kernel of Z_2s-linear hadamard codes

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	107-117
Number of pages	11
Journal	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
Publication status	Published - 2017

Keywords

Classification
Gray map
Hadamard code
Kernel
Z-additive code
Z-linear code

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

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title = "On the kernel of Z2s-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 = "Classification, Gray map, Hadamard code, Kernel, Z-additive code, Z-linear code",

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

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",

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TY - JOUR

T1 - On the kernel of Z2s-linear hadamard codes

AU - Fernández-Córdoba, Cristina

AU - Vela, Carlos

AU - Villanueva, Mercè

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 - Classification

KW - Gray map

KW - Hadamard code

KW - Kernel

KW - Z-additive code

KW - Z-linear code

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

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

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SP - 107

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ER -

On the kernel of Z_2s-linear hadamard codes

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Keywords

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