Canonization of linear codes over Z\mathbb ZZ4 (original) (raw)
Abstract
Two linear codes C,C′leqmathbbZC, C' \leq \mathbb ZC,C′leqmathbbZ4 n are equivalent if there is a permutation piinSn\pi \in S_npiinSn of the coordinates and a vector varphiin1,3n\varphi \in \{1,3\}^nvarphiin1,3n of column multiplications such that (varphi;pi)C=C′(\varphi; \pi) C = C'(varphi;pi)C=C′. This generalizes the notion of code equivalence of linear codes over finite fields.
In a previous paper, the author has described an algorithm to compute the canonical form of a linear code over a finite field. In the present paper, an algorithm is presented to compute the canonical form as well as the automorphism group of a linear code over mathbbZ\mathbb ZmathbbZ4. This solves the isomorphism problem for mathbbZ\mathbb ZmathbbZ_4_-linear codes. An efficient implementation of this algorithm is described and some results on the classification of linear codes over mathbbZ\mathbb ZmathbbZ4 for small parameters are discussed.
Mathematics Subject Classification: Primary: 05E20; Secondary: 20B25, 94B05.
Citation:
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References
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