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

Access to Document

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

Cite this

@article{aa2e2049617f43b8851c5212ccdf6662,

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",

journal = "Lecture Notes in Computer Science",

issn = "0302-9743",

}

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

UR - http://www.scopus.com/inward/record.url?scp=85028549729&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:85028549729

SP - 107

EP - 117

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -

On the kernel of Z_2s-linear hadamard codes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this