One-generator quasi-cyclic codes and their dual codes

Shivanshu Benjwal, Maheshanand Bhaintwal

Minjia Shi, Liqin Qian, Yan Liu +1 more

Chaofeng Guan, Ruihu Li, Liangdong Lü +2 more

Yu Yao, Yuena Ma, Husheng Li +1 more

In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes. By studying the form of Hermitian dual codes and their algebraic structure, we propose a sufficient condition for self-orthogonality of GQC codes with Hermitian inner product. By comparison, the quantum codes we constructed have better parameters than known codes.

P. Heijnen, F.M.J. Willems, T.J. Tjalkens

Wenyu Han, Tongjiang Yan, Yuhua Sun +2 more

This paper investigates a class of 4-generator quasi-cyclic (QC) codes of index 4, together with their duals under the Euclidean, Hermitian, and symplectic inner products. We derive explicit generator characterizations of their dual codes and establish sufficient conditions for dual containment. Based on these structural results, several new quantum stabilizer codes and quantum synchronizable codes with desirable parameters are constructed.