Two Classes of Linear Codes From Weil Sums

In this article, we consider two classes of
$p$
-ary linear codes. This article is a generalization of the recent construction methods given by Jian, Lin and Feng (2019). By choosing different defining sets, two classes of two-weight or three-weight linear codes over finite fields are constructed and their weight distributions are determined based on Weil sums. We also give some examples and some of the linear codes are almost optimal with respect to the Griesmer bound which can be directly employed to obtain democratic secret sharing schemes. Additionally, all nonzero codewords are minimal and they are crucial to apply in association schemes, strongly regular graphs, weakly regular plateaued functions and authentication codes.