论文标题
来自矢量布尔函数的最小二进制线性代码
Minimal Binary Linear Codes from Vectorial Boolean Functions
论文作者
论文摘要
最近，由于其偏爱秘密共享方案和安全的两党计算，因此已经取得了很大的进步来构建最小线性代码。在本文中，我们提出了一种新方法，通过使用矢量布尔函数来构建最小线性代码。首先，我们为矢量布尔函数的一类线性代码提供了必要和充分的条件。基于此，我们得出了一些新的三重量最小线性代码，并确定其重量分布。其次，我们从矢量布尔函数中获得了另一类通用的线性代码的必要条件，以至于最小并违反AB条件。结果，我们获得了三个无限的最小线性代码属于侵犯AB条件的家族。据我们所知，这是第一次由矢量布尔函数构建最小的衬里代码。与其他已知的相比，本文获得的最小衬里代码通常具有较高的尺寸。
Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put forward a new method to construct minimal linear codes by using vectorial Boolean functions. Firstly, we give a necessary and sufficient condition for a generic class of linear codes from vectorial Boolean functions to be minimal. Based on that, we derive some new three-weight minimal linear codes and determine their weight distributions. Secondly, we obtain a necessary and sufficient condition for another generic class of linear codes from vectorial Boolean functions to be minimal and to be violated the AB condition. As a result, we get three infinite families of minimal linear codes violating the AB condition. To the best of our knowledge, this is the first time that minimal liner codes are constructed from vectorial Boolean functions. Compared with other known ones, in general the minimal liner codes obtained in this paper have higher dimensions.
