论文标题
从部分差异集的最小线性代码构造
A construction of minimal linear codes from partial difference sets
论文作者
论文摘要
在本文中，我们研究了由有限场某些子集的特征函数定义的一类线性代码。我们得出了足够且必要的条件，使该代码通过字符理论方法是最小的线性代码。我们获得了新的三重量或四重的最小线性代码，这些代码无法通过使用部分差异集满足Ashikhmin-Barg条件。我们表明，我们的构造产生的最低线性代码不会因切割矢量阻塞集而产生，并在秘密共享方案中讨论了它们的应用。
In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical approach. We obtain new three-weight or four-weight minimal linear codes that do not satisfy the Ashikhmin-Barg condition by using partial difference sets. We show that our construction yields minimal linear codes that do not arise from cutting vectorial blocking sets, and also discuss their applications in secret sharing schemes.
