On the minimum number of minimal codewords

Titelangaben

dela Cruz, Romar ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
On the minimum number of minimal codewords.
In: Advances in Mathematics of Communications. Bd. 17 (2023) Heft 2 . - S. 333-341.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2020130

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Abstract

We study the minimum number of minimal codewords in linear codes using techniques from projective geometry. Minimal codewords have been used in decoding algorithms and cryptographic protocols. First, we derive a new lower bound on the number of minimal codewords. Then we give a formula for the minimum number of minimal codewords of linear codes for certain lengths and dimensions. We also determine the exact value of the minimum for a range of values of the length and dimension. As an application, we completed a table of the minimum number of minimal codewords for codes of length up to . Finally, we discuss an extension of the geometric approach to minimal subcode supports.