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Pàgina inicial > Articles > Articles publicats > Classification of the Z₂ Z₄-linear Hadamard codes and their automorphism groups |
Data: | 2015 |
Resum: | 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. |
Ajuts: | 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 |
Nota: | Combinatorics, Coding and Security Group (CCSG) |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Hadamard codes ; Z₂ Z₄-linear codes ; Additive codes ; Automorphism group |
Publicat a: | IEEE transactions on information theory, Vol. 61 Núm. 2 (Feb. 2015) , p. 887-894, ISSN 1557-9654 |
Post-print 8 p, 1.2 MB |