Classification of the Z2Z4-linear Hadamard codes and their automorphism groups Full article
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IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654 |
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| Output data | Year: 2015, Volume: 61, Number: 2, Pages: 887-894 Pages count : 8 DOI: 10.1109/tit.2014.2379644 | ||||||
| Tags | Hadamard codes, Z2Z4-linear codes, additive codes, automorphism group. | ||||||
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Abstract:
A Z2Z4-linear Hadamard code of length α+2β=2t is a binary Hadamard code, which is the Gray map image of a Z2Z4-additive code with α binary coordinates and β quaternary coordinates. 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. Moreover, the order of the monomial automorphism group for the Z2Z4-additive Hadamard codes and the permutation automorphism group of the corresponding Z2Z4-linear Hadamard codes are given
Cite:
Krotov D.S.
, Villanueva M.
Classification of the Z2Z4-linear Hadamard codes and their automorphism groups
IEEE Transactions on Information Theory. 2015. V.61. N2. P.887-894. DOI: 10.1109/tit.2014.2379644 WOS Scopus РИНЦ OpenAlex
Classification of the Z2Z4-linear Hadamard codes and their automorphism groups
IEEE Transactions on Information Theory. 2015. V.61. N2. P.887-894. DOI: 10.1109/tit.2014.2379644 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Aug 5, 2014 |
| Accepted: | Nov 19, 2014 |
| Published online: | Dec 10, 2014 |
Identifiers:
| Web of science: | WOS:000348298400015 |
| Scopus: | 2-s2.0-84921498113 |
| Elibrary: | 23968266 |
| OpenAlex: | W4300529123 |