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.
翻译：最近,在建立最低线性代码方面取得了很大进展,原因是他们偏爱秘密共享计划,并且确保双向计算。在本文件中,我们提出了一个新方法,通过使用矢量布尔函数来构建最低线性代码。首先,我们给从矢量布尔函数中得出的普通线性代码类别提供了必要和充分的条件,使从矢量布尔函数中获得的普通线性代码类别最小化。在此基础上,我们得出了一些新的三重最低线性代码并确定其重量分布。第二,我们获得了一个必要和充分的条件,使从矢量布尔函数中获得的另一种普通线性代码类别最小化并违反AB条件。结果,我们得到了三个违反AB条件的线性代码的无限组合。据我们所知,这是第一次从矢量布尔函数中构建最低线性代码。与其他已知的代码相比,一般来说,本文中获取的最低限度线性代码具有更高的维度。
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