2009/03/16 by Sergio R. López-Permouth, Sergio Lopez-Permouth, Lopez-Permouth, Sergio +2
Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Finite Group Theory Research #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0903.2791
Submitted
arxiv created 2009/03/16 · arxiv updated 2009/12/01
Repeated root Cyclic and Negacyclic codes over Galois rings have been studied much less than their simple root counterparts. This situation is beginning to change. For example, repeated root codes of length ps, where p is the characteristic of the alphabet ring, have been studied under some additional hypotheses. In each one of those cases, the ambient space for the codes has turned out to be a chain ring. In this paper, all remaining cases of cyclic and negacyclic codes of length ps over a Galois ring alphabet are considered. In these cases the ambient space is a local ring with simple socle but not a chain ring. Nonetheless, by reducing the problem to one dealing with uniserial subambients, a method for computing the Hamming distance of these codes is provided.