The b-symbol weight distributions of all semiprimitive irreducible cyclic codes

Abstract: Up to a new invariant $\mu(b)$, the complete $b$-symbol weight distribution of a particular kind of two-weight irreducible cyclic codes, was recently obtained by Zhu et al. [Des. Codes Cryptogr., 90 (2022) 1113-1125]. The purpose of this paper is to simplify and generalize the results of Zhu et al., and obtain the $b$-symbol weight distributions of all one-weight and two-weight semiprimitive irreducible cyclic codes.