Reed-Solomon group codes

摘要

Reed-Solomon codes over GF(pm), p a prime and m apositive integer, are cyclic maximum distance separable (MDS) and oflength pm-1. The additive group of GF(pm) iselementary abelian of type (1,1,...,1), isomorphic to a direct productof m cyclic groups of order p, denoted by C_pm.This paper deals with MDS codes over C_pm of lengthpm-1 which are cyclic and MDS, called Reed-Solomon groupcodes. In general, a group code over C_pm need notbe a linear code over GF(pm) as shown by an example