On the maximum number of minimal codewords

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dela Cruz, Romar ; Kurz, Sascha:
On the maximum number of minimal codewords.
In: Discrete Mathematics. Bd. 344 (2021) Heft 9 . - 112510.
ISSN 0012-365X
DOI: https://doi.org/10.1016/j.disc.2021.112510

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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 k and length k+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 k and length k+3.