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 $k+3$.

中文翻译：

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关于最小码字的最大数目

最小码字可用于解码线性代码和密码学。我们研究给定长度和维度的二进制线性代码中最小码字的最大数量。提出了最大数量的改进下限和上限。我们确定维度k和长度的线性代码情况的确切值$克+2$以及长度和尺寸的小值。我们还给出了维度k和长度的线性码的最小码字数的公式$克+3$.