# Multivariable codes over finite chain rings: semisimple codes

Research paper by E. Martinez-Moro, I. F. Rua

Indexed on: 24 May '05Published on: 24 May '05Published in: Mathematics - Combinatorics

#### Abstract

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.