线性码被广泛应用于通信中的差错控制, 数据储存, 量子码构造等多个领域. 线性码重量分布一直是线性码研究的一个重要课题. 文章确定了由二次完全非线性函数构造的线性码的完全重量分布; 证明了两类循环码的完全重量分布可以从其重量分布直接得到.

Linear codes have been widely used in error control of communications, data storage and construction of quantum codes, and so on. The study of weight distribution of linear codes is always an important research topic on linear codes. This paper determines complete weight distribution of a class of linear codes constructed from perfect nonlinear quadratic polynomials and proves that the complete weight distributions of two classes of linear codes can be derived from their weight distributions.