论文标题
最大数量的最小代码字数
On the maximum number of minimal codewords
论文作者
论文摘要
最小的代码字在解码线性代码和密码学中具有应用。我们研究给定长度和尺寸的二进制线性代码中最小代码字数。提出了最大数量上的上限和上限。我们确定尺寸$ k $和长度$ k+2 $的线性代码的确切值以及长度和尺寸的小值。我们还提供了一个公式，以最小的尺寸线性代码$ k $和长度$ k+3 $的线性代码。
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 $k+3$.
