Weight distributions of generalized quasi-cyclic codes over Fq+uFq

In this paper, by Gauss sums, we determine Hamming weight distributions of generalized quasi-cyclic (GQC) codes over the finite chain ring F q + u F q, where u 2 = 0. As applications, some new infinite families of minimal linear codes with W min W max ≤ q − 1 q and projective two-weight codes are constructed.