On binary linear codes and binary pseudo-random sequences

Abstract

In this paper, we study the relation between the linear subspace of the pseudo-noise (PN)-sequences generated by a primitive polynomial and the simplex code. This family of sequences can be also seen as an Maximum Distance Separable (MDS) [Formula: see text]-linear code over [Formula: see text]. Furthermore, we see how to compute the family of generalized sequences produced by a primitive polynomial by means of a first-order Reed–Muller code.