Several classes of linear codes with a few weights from defining sets over Fp plus uFp

Recently, linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. Results have shown that some optimal codes can be acquired if the defining sets are well chosen over finite fields. In this paper, we investigate the Lee-weight distribution of linear codes over the ring Fp+uFp (p is an odd prime) based on defining sets by employing exponential sums. We then determine the explicit complete weight enumerator for the images of these linear codes under the Gray map. A class of constant weight codes that meets the Griesmer bound for constructing optimal constant composition codes achieving the LVFC bound is also presented.