Classification of the Z2Z4-linear Hadamard codes and their automorphism groups

Denis S. Krotov, Merce Villanueva

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

© 1963-2012 IEEE. 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 ⌊t2⌋ 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 ⌊t2⌋ 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.
Original languageEnglish
Article number6981977
Pages (from-to)887-894
JournalIEEE Transactions on Information Theory
Volume61
Issue number2
DOIs
Publication statusPublished - 1 Feb 2015

Keywords

  • Hadamard codes
  • Z Z -linear codes 2 4
  • additive codes
  • automorphism group

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