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Computer Science > Information Theory

arXiv:2212.14225 (cs)
[Submitted on 29 Dec 2022 (v1), last revised 11 Nov 2024 (this version, v4)]

Title:Symplectic self-orthogonal quasi-cyclic codes

Authors: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.
Subjects: Information Theory (cs.IT)
Cite as: arXiv:2212.14225 [cs.IT]
  (or arXiv:2212.14225v4 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2212.14225

Submission history

From: Chaofeng Guan [view email]
[v1] Thu, 29 Dec 2022 08:48:56 UTC (199 KB)
[v2] Sun, 8 Jan 2023 11:42:11 UTC (495 KB)
[v3] Mon, 23 Oct 2023 03:57:29 UTC (41 KB)
[v4] Mon, 11 Nov 2024 07:20:04 UTC (642 KB)
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