Abstract: Linear codes with a few weights have important applications in secret sharing schemes, authentication codes, association schemes, and strong regular graphs. A class of 3-weight or 4-weight linear codes is provided with Boolean functions. The parameters and weight distributions of these codes are determined by the theory of character sums and the Walsh spectrum of Boolean functions. The proposed 3-weight codes can be used to construct secret sharing schemes and association schemes. The dual codes of the provided codes are optimal or almost optimal with respect to the sphere-packing bound.

Key words: linear code, weight distribution, Weil sum, boolean function, Walsh transform