论文标题
三重二进制线性代码的几个家族的重量分布
Weight distributions of several families of 3-weight binary linear codes
论文作者
论文摘要
具有几个权重的线性代码已广泛应用于组合设计，秘密共享，关联方案，身份验证代码和强烈规则的图表中。在本文中，我们首先纠正有关指数总和$ \ sum_ {x \ in \ mathbb {f} _ {2^{e}}χ_1\ left（ax^{2^α+1}+bx \ right）的错误结果。此外，其中大多数可以用于秘密共享方案。
The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the exponential sum $\sum_{x\in \mathbb{F}_{2^{e}}}χ_1\left(ax^{2^α+1}+bx\right).$ Then, using the above exponential sum, we construct several families of binary linear codes of $3$-weight and determine their weight distributions. Moreover, Most of them can be used in secret sharing schemes.
