In this paper, we will give the generic construction of a binary linear code of dimension $n+3$ and derive the necessary and sufficient conditions for the constructed code to be minimal. Using generic construction, a new family of minimal binary linear code will be constructed from a special class of Boolean functions violating the Ashikhmin-Barg condition. We also obtain the weight distribution of the constructed minimal binary linear code.

翻译：本文将对维数为$n+3$的二元线性码进行一般性构造，并给出所构造码为极小码的充要条件。通过该一般性构造，我们将从一类违反Ashikhmin-Barg条件的特殊布尔函数出发，构造出一族新的极小二元线性码。同时，我们还得到了所构造极小二元线性码的权重分布。