Multivariable Codes Over Finite Chain Rings: Serial Codes
Edgar Martı́nez-Moro, I. F. Rúa · SIAM Journal on Discrete Mathematics · 2006
The structure of multivariate serial 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 nontrivial codes over R. The structure of the dual codes in the serial abelian case is also derived, and some conditions for the existence of self‐dual codes over R are studied.