Contents I. Introduction
Let be an linear code over For any pair of codewords , the rank distance between them is defined to be the rank over of the matrix corresponding to obtained by expanding each entry of as an m-tuple along a basis of over and is denoted by [2]. The rank of , denoted by is defined as the minimum of over all possible pairs of distinct codewords. Rank-distance codes over finite fields have been studied by several authors for applications in storage devices and more recently for applications in Space-Time coding. These studies are for the general class of linear codes and hence specific results like expressions or bounds for the rank of the code given by the description of the code are not known. In view of this, in this paper, we focus on primitive length cyclic codes over and obtain expressions and upper bounds for the rank-distance of few sub classes of these codes. Note that this class of codes includes the well known Reed-Solomon codes.
