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：本文提供了通用的Mattson Solomon 多元圆环对当地圆环的多次根多环编码,从完成单一根研究的一流能力来看,这些编码明显分解了它们,并用矩阵产品编码说明了重复根多环编码对有限领域的一些结构特性,两种方法都描述了特定多环代码的$\perp_0美元双向编码。