Symplectic self-orthogonal quasi-cyclic codes

Chaofeng Guan; Ruihu Li; Jingjie Lv; Zhi Ma

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arXiv · 2212.14225

Symplectic self-orthogonal quasi-cyclic codes

Chaofeng Guan·Ruihu Li·Jingjie Lv·Zhi Ma

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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 $1$-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 $117$ record-breaking quantum error-correction codes.

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Chaofeng Guan, Ruihu Li, Jingjie Lv, Zhi Ma. 2022-12-29. Symplectic self-orthogonal quasi-cyclic codes. https://arxiv.org/abs/2212.14225

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