Classification of type IV self-dual \(\mathbb{Z}_4\)-codes of length 16
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.
scientific article; zbMATH DE number 1538399