On the structure of repeated-root polycyclic codes over local rings

Abstract

This paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the ⊥0-dual code for a given polycyclic code. © 2023 Elsevier B.V.