English

On the maximum number of minimal codewords

Information Theory 2020-10-22 v1 Combinatorics math.IT

Abstract

Minimal codewords have applications in decoding linear codes and in cryptography. We study the maximum number of minimal codewords in binary linear codes of a given length and dimension. Improved lower and upper bounds on the maximum number are presented. We determine the exact values for the case of linear codes of dimension kk and length k+2k+2 and for small values of the length and dimension. We also give a formula for the number of minimal codewords of linear codes of dimension kk and length k+3k+3.

Keywords

Cite

@article{arxiv.2010.10762,
  title  = {On the maximum number of minimal codewords},
  author = {Romar dela Cruz and Sascha Kurz},
  journal= {arXiv preprint arXiv:2010.10762},
  year   = {2020}
}

Comments

13 pages, 1 table

R2 v1 2026-06-23T19:30:37.409Z