Subspace subcodes of Reed-Solomon codes

A subspace subcode of a Reed-Solomon (SSRS) code over GF(2m) is the set of RS code-words, whose components all lie in a particular GF(2)-subspace of GF(2m). SSRS codes include both generalized BCH codes and “trace-shortened” RS codes as special cases. In this paper we present an explicit formula for the dimension of an arbitrary RS subspace subcode. Using this formula, we find that in many cases, SSRS codes are competitive with algebraic geometry codes, and that in some cases, the dimension of the best subspace subcode is larger than that of the corresponding GBCH code