On the automorphism groups of the Z₂Z₄-linear Hadamard codes and their classification

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...

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Bibliographic Details
Authors: Krotov, Denis S., Villanueva, M.|||0000-0001-6179-0833
Format: book part
Publication Date:2015
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:142876
Online Access:https://ddd.uab.cat/record/142876
https://dx.doi.org/urn:doi:10.1007/978-3-319-17296-5_25
Access Level:Open access
Keyword:Z₂Z₄-linear codes
Additive codes
Hadamard codes
Automorphism group
Description
Summary: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 orders of the permutation automorphism groups of the Z₂Z₄-linear Hadamard codes are given.