Several classes of new projective three-weight or four-weight linear codes and their applications in $ s $-sum sets

Abstract

In this paper, let $ q $ be a power of a prime, we construct several classes of new projective three-weight or four-weight linear codes over $ \mathbb{F}_q $ from the defining sets construction, and determine their weight distributions by using additive character sums. Especially, these codes are suitable for applications in secret sharing schemes. Furthermore, basing on two classes of projective three-weight codes, we construct some $ s $-sum sets for any odd $ s>1 $.