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In this paper, for an odd prime $p$, by extending Li et al.'s construction\cite{CL2016}, several classes of two-weight and three-weight linear codes overthe finite field $\mathbb{F}_p$ are constructed from a defining set, and thentheir complete weight enumerators are determined by using Weil sums.Furthermore, we show that some examples of these codes are optimal or almostoptimal with respect to the Griesmer bound. Our results generalize thecorresponding results in \cite{CL2016, GJ2019}.

Complete weight enumerators for several classes of two-weight and three-weight linear codes