Linear codes over finite rings are trace codes

Linear codes over finite rings are described here as trace codes for a suitable generalization of the trace called a GF-trace. Cyclic codes over Galois rings are given a trace description as well. The main tools are the notion of trace dual bases, in the case of linear codes, and of normal bases of...

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Bibliographic Details
Published in:Discrete mathematics 2020-08, Vol.343 (8), p.111919, Article 111919
Main Authors: Lu, Yaqi, Shi, Minjia, Greferath, Marcus, Solé, Patrick
Format: Article
Language:English
Subjects:
Basis
Commutative Algebra
Cyclic codes
Finite ring
GF-trace
Linear codes
Mathematics
Trace representation
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Summary:Linear codes over finite rings are described here as trace codes for a suitable generalization of the trace called a GF-trace. Cyclic codes over Galois rings are given a trace description as well. The main tools are the notion of trace dual bases, in the case of linear codes, and of normal bases of an extension ring over a ring, in the case of cyclic codes.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.111919