Repeated Root Cyclic and Negacyclic Codes over Galois Rings

摘要

In this notice we describe the ideal structure of all cases of cyclic and negacyclic codes of length p~s over a Galois ring alphabet that have not yet been discussed in the literature. Unlike in the cases reported earlier in the literature by various authors, the ambient spaces here are never chain rings. These ambient rings do nonetheless share the properties of being local and having a simple socle.