Abstract: Recently, linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes, constant composition codes, strongly regular graphs and so on. In this paper, based on the Weil sums, several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set, and their weight enumerators and complete weight enumerators are determined. Furthermore, these codes are proven to be minimal. By puncturing these linear codes, two classes of two-weight projective codes are obtained, and the parameters of the corresponding strongly regular graph are given. This paper generalizes the results of [7].

Key words: Weil sum, Linear code, Complete weight enumerator, Minimal code, Strongly regular graph