Reed-Solomon group codes

Reed-Solomon codes over GF(p/sup m/), p a prime and m a positive integer, are cyclic maximum distance separable (MDS) and of length p/sup m/-1. The additive group of GF(p/sup m/) is elementary abelian of type (1,1,...,1), isomorphic to a direct product of m cyclic groups of order p, denoted by C/sub p//sup m/. This paper deals with MDS codes over C/sub p//sup m/ of length p/sup m/-1 which are cyclic and MDS, called Reed-Solomon group codes. In general, a group code over C/sub p//sup m/ need not be a linear code over GF(p/sup m/) as shown by an example.