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

Abstract: In this paper, based on the theory of defining sets, a class of four-weight or five-weight linear codes over Fp is constructed. The complete weight enumerators of the linear codes are determined by means of 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. This is an extension of the results raised by Zhang et al.(2020).