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

In this paper, for an odd prime p, by extending Li et al.'s construction [17], several classes of two-weight and three-weight linear codes over the finite field Fp are constructed from a defining set, then their complete weight enumerators determined using Weil sums. Furthermore, we show that some examples these optimal or almost with respect to Griesmer bound. Our results generalize corresponding in [15], [17].