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On the maximum number of minimal codewords

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arxiv 2010.10762 v1 pith:MQ4U2CK5 submitted 2020-10-21 cs.IT math.COmath.IT

Romar dela Cruz , Sascha Kurz This is my paper · ORCID
classification cs.ITmath.COmath.IT
keywords codescodewordsdimensionlengthlinearminimalnumbermaximum
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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 $k+3$.

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