On The Dimension of SSRS Codes

A subspace subcode of Reed-Solomon (SSRS) [1] code is a subcode of a Reed-Solomon (RS) code (called the parent code) over $F_{p^m}$ consisting of codewords whose components all lie in a fixed v-dimensional $(over\hspace{5mm}F_p;\hspace{5mm}p-\hspace{5mm}a\hspace{5mm}prime)$ vector subspace V of $F_{p^}m$. In this paper we present a formula for the cardinality of an SSRS code by viewing V as an [m,v] linear code over $F_p$ with parity check matrix H. Our formula is in terms of H and counting the endomorphisms of $F_{p^m}$ satisfying certain conditions resulting from the DFT domain characterization of SSRS code