Per citar aquest document: http://ddd.uab.cat/record/142691
Construction of Hadamard Z₂Z₄Q₈-codes for each allowable value of the rank and dimension of the kernel
Montolio, Pere (Universitat Oberta de Catalunya)
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Data: 2015
Resum: This work deals with Hadamard Z₂Z₄Q₈-codes, which are binary codes after a Gray map from a subgroup of a direct product of Z₂, Z₄ and Q₈ groups, where Q₈ is the quaternionic group. In a previous work, these kind of codes were classified in five shapes. In this paper we analyze the allowable range of values for the rank and dimension of the kernel, which depends on the particular shape of the code. We show that all these codes can be represented in a standard form, from a set of generators, which help to understand the characteristics of each shape. The main results we present are the characterization of Hadamard Z₂Z₄Q₈-codes as a quotient of a semidirect product of Z₂Z₄-linear codes and, on the other hand, the construction of Hadamard Z₂Z₄Q₈-codes with each allowable pair of values for the rank and dimension of the kernel.
Nota: Número d'acord de subvenció MICINN/TIN2013-40524-P
Nota: Número d'acord de subvenció AGAUR/2014/SGR-691
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; acceptedVersion
Matèria: Combinatorial mathematics ; Dimension of the kernel ; Error-correcting codes ; Hadamard codes ; Rank ; Z₂Z₄-codes ; Z₂Z₄Q₈-codes
Publicat a: IEEE transactions on information theory, Vol. 61 Issue 4 (April 2015) , p. 1948-1958, ISSN 0018-9448

DOI: 10.1109/TIT.2015.2398869


Post-print
19 p, 1.9 MB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Enginyeries > Combinatorics, Coding and Security Group (CCSG)
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 Registre creat el 2015-11-03, darrera modificació el 2016-06-09



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