Generalized weights and the Ball-Blokhuis congruence

Abstract

In a 2013 article, Ball and Blokhuis proved a congruence for a linear [n, k] code with a codeword of weight n. Their proof is based on a character sum on the group of 1 x (k-1) nonzeromatrices. We showthat the same argumentworks for groups of r x (k-1) matrices for every r, 1 <= r <= k. So we extend their theorem by giving a family of k congruences.