Abstract: It is of vital significance to explore the weight distributions of linear codes with a few weights in coding theory. By selecting an appropriate defining set, a new class of two-weight or three-weight linear codes is constructed. Then, their weight distributions are determined by employing exponential sums over finite fields. Furthermore, some examples to verify the correctness of our results were gived and some of them are optimal codes with respect to the Griesmer bound.

Key words: linear code, weight distribution, Weil sums, Griesmer bound, optimal code