Information sets for abelian codes

Abstract

All throughout F denotes the field with q elements where q is a power of a prime p. Given C, a linear code of dimension k, and length n over the field F, an information set for C is a set of positions {i1, …, ik} such that restricting the codewords to these positions we get the hole space Fk. The codeword symbols in these positions are called information symbols and the other n — k positions are called check positions ([10]).