Classification of type IV self-dual \(\mathbb{Z}_4\)-codes of length 16
type: Item
instance of: scholarly article
title: Classification of type IV self-dual \(\mathbb{Z}_4\)-codes of length 16
zbMATH Open document ID: 0961.94014
author: Masaaki Harada
author: Akihiro Munemasa
published in: Finite Fields and their Applications
publication date: 2001-05-16T00:00:00Z
review text: Self-dual codes over \(\mathbb Z_4\) have earlier been classified up to length 15. For length 16, \textit{V. Pless, J. S. Leon} and \textit{J. Fields} [J. Comb. Theory, Ser. A 78, 32-50 (1997; Zbl 0872.94050)] classified Type II self-dual codes, and in the current paper Type IV codes -- whose codewords have even Hamming weight -- are considered. There are 11 inequivalent such codes (5 of which are Type II); these codes and their main parameters are described. The following result is proved and utilized in the classification: The Type IV self-dual \(\mathbb Z_4\)-codes of length \(n\) are in one-to-one correspondence with the binary Type II codes of length \(2n\) satisfying some condition and containing a fixed-point-free involution in the automorphism group.
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 1538399
zbMATH Keywords: code equivalence
zbMATH Keywords: codes over \(\mathbb Z_4\)
zbMATH Keywords: self-dual codes
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
full work available at URL: ffta.2000.0279
OpenAlex ID: W2059088631
cites work: Type II codes over Z/sub 4/
cites work: The binary self-dual codes of length up to 32: A revised enumeration
cites work: Self-dual codes over the integers modulo 4
cites work: Type IV self-dual codes over rings
cites work: All self-dual Z/sub 4/ codes of length 15 or less are known
cites work: Mass formulas for self-dual codes over Z/sub 4/ and F/sub q/+uF/sub q/ rings
cites work: Q4495693
cites work: All \(\mathbb{Z}_ 4\) codes of type II and length 16 are known
DOI: 10.1006/FFTA.2000.0279
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description: scientific article; zbMATH DE number 1538399