论文标题
布尔功能的二进制线性代码很少
Binary linear codes with few weights from Boolean functions
论文作者
论文摘要
布尔功能在密码学和编码理论中具有非常好的应用，这导致了许多研究关注其应用的研究。本文的目的是构建定义集的重量很少的二进制线性代码，该代码由一些特殊的布尔功能和一些其他限制来定义。首先，我们提供了两个二进制线性代码的一般构造，其中包含来自布尔函数的三个或四个权重，最多具有三个walsh变换值，并确定其双重代码的参数。然后，获得了许多具有明确权重枚举器的二进制线性代码。某些二进制线性代码及其双重代码是最佳或几乎最佳的。本文获得的二进制线性代码可能对秘密共享方案，关联方案和强烈规则图具有特别的兴趣。
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the defining set, which is defined by some special Boolean functions and some additional restrictions. First, we provide two general constructions of binary linear codes with three or four weights from Boolean functions with at most three Walsh transform values and determine the parameters of their dual codes. Then many classes of binary linear codes with explicit weight enumerators are obtained. Some binary linear codes and their duals obtained are optimal or almost optimal. The binary linear codes obtained in this paper may have a special interest in secret sharing schemes, association schemes, strongly regular graphs.
