Constructions of projective linear codes by the intersection and difference of sets

Projective linear codes are a special class of linear codes whose dual codes have minimum distance at least 3. Projective linear codes with only a few weights are useful in authentication codes, secret sharing schemes, data storage systems and so on. In this paper, two constructions of q-ary linear codes are presented with defining sets given by the intersection and difference of two sets. These constructions produce several families of new projective two-weight or three-weight linear codes. As applications, our projective codes can be used to construct secret sharing schemes with interesting access structures, strongly regular graphs and association schemes with three classes.