Repeated-root cyclic and negacyclic codes over a finite chain ring

2006-08-21T17:44:08Z (GMT) by A.M. Salagean
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring.