Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic functions via a bivariate construction and then determine the complete weight enumerators and weight hierarchies of these linear codes completely. This paper generalizes some results in Li et al. (2022) and Hu et al. (2024).

翻译：具有少量重量的线性码可应用于秘密共享、认证码、关联方案和强正则图。对于奇素数幂$q$，我们通过双变量构造方法，从二次函数构建了一类三重重量$\F_q$-线性码，然后完整确定了这些线性码的完全重量计数器和重量层次结构。本文推广了Li等人（2022）和Hu等人（2024）中的部分结果。