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In this paper, based on the theory of defining sets, a class of four-weightor five-weight linear codes over Fp is constructed. The complete weightenumerators of the linear codes are determined by means of Weil sums. In somecase, there is an almost optimal code with respect to Griesmer bound, which isalso an optimal one according to the online code table. This is an extension ofthe results raised by Zhang et al.(2020).

Complete weight enumerators of a class of linear codes with four or five weights