Reed-Solomon group codes

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