一类基于向量布尔函数构造的极小二无线性码

Minimal Binary Linear Codes from a Class of Vectorial Boolean Functions

线性码在数据储存、通信、密码学和组合数学等方面都有着重要的应用, 其中的极小线性码可以用 来构造具有良好访问结构的秘密共享方案. 本文利用向量布尔函数构造了一类新的二无线性码, 并且利用布尔函数的密码学性质研究了线性码的长度, 维数和重量分布. 结论表明, 所构造的线性码 最小距离更大且为宽极小码. 此外, 本文将现有的一些结果推广到一般情形.

The applications of linear codes in data storage, communication, cryptography and combinatorial mathematics have been of great importance over the years, among which minimal linear codes can be used to construct secret sharing schemes with good ac- cess structure. In this paper, we construct a new class of binary linear codes using vectorial Boolean functions, and study the length, dimension and weight distribution of linear codes using the cryptographic properties of Boolean functions. The results show that the constructed linear codes have larger minimum distance and are wide minimal codes. At the same time, this article extends some existing results to general situations.