In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums. In some case, there is an almost optimal code with respect to Griesmer bound, which is also an optimal one according to the online code table. The linear codes can also be employed to get secret sharing schemes.

翻译：本文基于定义集理论，构造了$\mathbb{F}_p$上的两类至多六权线性码。通过高斯周期与Weil和，确定了这些线性码的权值分布。在特定情形下，存在关于Griesmer界几乎最优的码，该码根据在线码表亦为最优码。此类线性码还可用于构建秘密共享方案。