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...
| Authors: | , |
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| 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 |
| 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. |
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