On normalized generating sets for GQC codes over Z(2)

Abstract

Let r(i), be positive integers and R-i = Z(2)[x]/ < x(ri) - 1 > for 1 <= i <= l. Denote R = R-1 x R-2 x ... x R-l. Generalized quasi-cyclic (GQC) code C of length (r(1), r(2),..., r(l)) over Z(2) can be viewed as Z(2) [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. (C) 2016 Elsevier Inc. All rights reserved.