Multivariable codes over finite chain rings: semisimple codes

Details Multivariable codes over finite chain rings: semisimple codes Multivariable codes over finite chain rings: semisimple codes

2005-05-24

arxiv.org/abs/math/0505491v1

Mathematics

Combinatorics

Submitted to SIAM Journal on Discrete Mathematics

Scientific paper

The structure of multivariate semisimple codes over a finite chain ring $R$ is established using the structure of the residue field $\bar R$. Multivariate codes extend in a natural way the univariate cyclic and negacyclic codes and include some non-trivial codes over $R$. The structure of the dual codes in the semisimple abelian case is also derived and some conditions on the existence of selfdual codes over $R$ are studied.

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