论文标题
来自弱规则平衡功能的最小线性代码
Minimal Linear Codes From Weakly Regular Plateaued Balanced Functions
论文作者
论文摘要
线性代码在秘密共享方案，安全的两党计算，关联方案，非常规则的图表，身份验证代码和通信中具有多种应用。文献中有大量的线性代码很少，但其中少量是最小的。在本文中，我们首次在线性代码的第二个通用构造方法中首次使用奇数特征的有限特征的有限特征的平衡函数。本文的主要结果如下所述。我们首先构建了几个三重量和四重的线性代码，该代码具有弱规则平衡函数的灵活参数。值得注意的是，可以从这些功能中获得（几乎）最佳代码。接下来，我们观察到本文获得的所有代码都是最小的，因此可以直接雇用它们来建立秘密共享计划，以高民主。最后，民主的秘密共享计划是从我们最少代码的双重代码中获得的。
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights in the literature, but a little of them are minimal. In this paper, we are using for the first time weakly regular plateaued balanced functions over the finite fields of odd characteristic in the second generic construction method of linear codes. The main results of this paper are stated below. We first construct several three-weight and four-weight linear codes with flexible parameters from weakly regular plateaued balanced functions. It is worth noting that the (almost) optimal codes may be obtained from these functions. We next observe that all codes obtained in this paper are minimal, thereby they can be directly employed to construct secret sharing schemes with high democracy. Finally, the democratic secret sharing schemes are obtained from the dual codes of our minimal codes.
