Quasi~λ-cyclic Codes Over a Class of Finite Commutative Semi-simple Rings

Abstract

In coding theory, quasi λ-cyclic codes form an important class of codes which have been extensively studied. In this paper, we investigate the algebraic structure of quasi λ-cyclic codes over finite commutative semi simple rings. And we establish the relationship between quasi λ-cyclic codes over finite commutative semi-simple ring R and quasi λ-cyclic codes over finite fields Fq. Furthermore, we decompose quasi λ-cyclic codes to a direct sum of component codes C linear codes over rings, give the decomposition of quasi λ-cyclic codes and describe its dual codes.