Multivariable codes over finite chain rings: semisimple codes
arXiv:math/0505491
Abstract
The structure of multivariate semisimple codes over a finite chain ring is established using the structure of the residue field . Multivariate codes extend in a natural way the univariate cyclic and negacyclic codes and include some non-trivial codes over . The structure of the dual codes in the semisimple abelian case is also derived and some conditions on the existence of selfdual codes over are studied.
Submitted to SIAM Journal on Discrete Mathematics