Primitive idempotents and constacyclic codes over finite chain rings

  • Mohammed Charkani Department of Mathematics, Faculty of Sciences Dhar-Mahraz, University Sidi Mohamed Ben Abdellah
  • Joel Kabore Department of Mathematics, University Joseph Ki-Zerbo
Keywords: finite chain ring, idempotent, constacyclic code, self-dual code

Abstract

Let R be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of R[X]/ <g> where g is a regular polynomial in R[X]. We use this set to decompose the ring R[X]/ <g> and to give the structure of constacyclic codes over finite chain rings. This allows us to describe generators of the dual code C' of a constacyclic code C and to characterize non-trivial self-dual constacyclic codes over finite chain rings.

Published
2020-09-01
How to Cite
Charkani, M., & Kabore, J. (2020). Primitive idempotents and constacyclic codes over finite chain rings. Gulf Journal of Mathematics, 8(2), 55-67. Retrieved from https://gjom.org/index.php/gjom/article/view/434
Section
Articles