Generalized weights and the Ball-Blokhuis congruence


ÖZEN İ.

DESIGNS CODES AND CRYPTOGRAPHY, vol.79, no.2, pp.231-235, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 79 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s10623-015-0046-x
  • Title of Journal : DESIGNS CODES AND CRYPTOGRAPHY
  • Page Numbers: pp.231-235

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.