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 that completes the single root study. 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 $\perp_0$-dual code of a given polycyclic code.

翻译：本文给出了局部环上重根多循环码的广义Mattson Solomon多项式，该多项式通过幂等元给出了这些码的显式分解，从而完善了单根情形的研究。同时，本文以矩阵乘积码的形式阐述了有限域上重根多循环码的若干结构性质。这两种方法均提供了给定多循环码的$\perp_0$-对偶码的描述。