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Classification of the Z₂ Z₄-linear Hadamard codes and their automorphism groups
Krotov, Denis S. (Sobolev Institute of Mathematics)
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Date: 2015
Abstract: A Z₂ Z₄-linear Hadamard code of length α + 2β = 2t is a binary Hadamard code, which is the Gray map image of a Z₂ Z₄-additive code with α binary coordinates and β quaternary coordinates. It is known that there are exactly ⌊t-1/2⌋ and ⌊t/2⌋ nonequivalent Z₂ Z₄-linear Hadamard codes of length 2t, with α = 0 and α ≠ 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z₂ Z₄-linear Hadamard code with α = 0 is equivalent to a Z₂ Z₄-linear Hadamard code with α ≠ 0, so there are only ⌊t/2⌋ nonequivalent Z₂ Z₄-linear Hadamard codes of length 2t. Moreover, the order of the monomial automorphism group for the Z2Z4-additive Hadamard codes and the permutation automorphism group of the corresponding Z₂ Z₄-linear Hadamard codes are given.
Grants: Ministerio de Ciencia e Innovación TIN2010-17358
Ministerio de Ciencia e Innovación TIN2013-40524-P
Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691
Note: Combinatorics, Coding and Security Group (CCSG)
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Subject: Hadamard codes ; Z₂ Z₄-linear codes ; Additive codes ; Automorphism group
Published in: IEEE transactions on information theory, Vol. 61 Núm. 2 (Feb. 2015) , p. 887-894, ISSN 0018-9448

DOI: 10.1109/TIT.2014.2379644


Post-print
8 p, 1.2 MB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Engineering > Combinatorics, Coding and Security Group (CCSG)
Articles > Research articles
Articles > Published articles

 Record created 2015-10-06, last modified 2022-09-04



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