Symplectic self-orthogonal quasi-cyclic codes
Information Theory
2025-06-10 v5 math.IT
Abstract
In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of -generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct numerous new binary symplectic self-orthogonal QC codes with excellent parameters, leading to record-breaking quantum error-correction codes.
Cite
@article{arxiv.2212.14225,
title = {Symplectic self-orthogonal quasi-cyclic codes},
author = {Chaofeng Guan and Ruihu Li and Jingjie Lv and Zhi Ma},
journal= {arXiv preprint arXiv:2212.14225},
year = {2025}
}
Comments
This paper was published in IEEE TIT. In this version, we have corrected some minor errors, among which the most significant change is that the constraint $\gcd(\bar{f}_0(x),g(x))=1$ in Theorem 5 has been corrected to $\gcd(f_0(x),g(x))=1$