On normalized generating sets for GQC codes over Z2

Let ri be positive integers and Ri=Z2[x]/〈xri−1〉 for 1≤i≤ℓ. Denote R=R1×R2×⋯×Rℓ. Generalized quasi-cyclic (GQC) code C of length (r1,r2,…,rℓ) over Z2 can be viewed as Z2[x]-submodule of R. In this paper, we investigate the algebraic structure of C by presenting its normalized generating set. We also present a method to determine the normalized generating set of the dual code of C, which is derived from the normalized generating set of C.