A Class of Linear Codes with Three and Five Weights

Linear codes have been an interesting topic in both theory and practice for many years. Based on the theory of defining set, a class of three-weight and five-weight linear codes over prime field F_p are constructed, which is an extension of Wang et al.'s construction. Our construction include some optimal codes and almost optimal codes with respect to the Singleton bounds. We employ exponential sums to investigate the weight distributions of these linear codes. The results show that these codes can be used to construct secret sharing schemes.