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7 p, 576.8 KB

Hadamard Z₂Z₄Q₈-codes : rank and 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)
Hadamard Z₂Z₄Q₈-codes are Hadamard binary codes coming from a subgroup of the direct product of Z₂, Z₄ and Q ₈ groups, where Q ₈ is the quaternionic group. We characterize Hadamard Z₂Z₄Q₈-codes as a quotient of a semidirect product of Z₂Z₄-linear codes and we show that all these codes can be represented in a standard form, from a set of generators. [...]
Springer 2015 (CIM Series in Mathematical Sciences) - DOI (Digital Object Identifier)

10.1007/978-3-319-17296-5_29
Coding Theory and Applications. Palmela Castle, Portugal, Vol. 3, 2015 , p. 273-279

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7 p, 1002.4 KB

On the automorphism groups of the Z₂Z₄-linear Hadamard codes and their classification / Krotov, Denis S. (Sobolev Institute of Mathematics) ; Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
It is known that there are exactly ⌊(t−1)/2⌋ and ⌊t/2⌋ nonequivalent Z₂Z₄-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 Z₂Z₄-linear Hadamard code with α = 0 is equivalent to a Z₂Z₄-linear Hadamard code with α ≠ 0, so there are only ⌊t/2⌋ nonequivalent Z₂Z₄-linear Hadamard codes of length 2ᵗ. [...]
Springer 2015 (CIM Series in Mathematical Sciences) - DOI (Digital Object Identifier)

10.1007/978-3-319-17296-5_25
Coding Theory and Applications, Vol. 3, 2015, p. 237-243

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