On the maximum number of minimal codewords

10/21/2020

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by   Romar dela Cruz, et al.

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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.