On MDS color codes

被引：0

作者：

de Albuquerque, Clarice Dias ^{[1
]}

Vieira, Vandenberg Lopes ^{[2
]}

Oliveira Quilles Queiroz, Catia Regina de ^{[3
]}

La Guardia, Giuliano Gadioli ^{[4
]}

de Oliveira, Anderson Jose ^{[3
]}

de Lima, Leandro Bezerra ^{[5
]}

机构：

[1] Fed Univ Cariri UFCA, Ctr Sci & Technol, BR-63048080 Juazeiro Do Norte, CE, Brazil

[2] State Univ Paraiba UEPB, Dept Math, BR-58429500 Campina Grande, PB, Brazil

[3] Fed Univ Alfenas UNIFAL MG, Inst Exact Sci, Dept Math, BR-37130000 Alfenas, MG, Brazil

[4] State Univ Ponta Grossa UEPG, Dept Math & Stat, BR-84030900 Ponta Grossa, PR, Brazil

[5] Fed Univ Mato Grosso Sul UFMS, Inst Math, BR-79070900 Campo Grande, MS, Brazil

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2022年 / 599卷

关键词：

Topological codes; Surface codes; Quantum codes;

D O I：

10.1016/j.physa.2022.127433

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this note, we show that the unique class of color codes whose parameters attain the quantum Singleton bound (MDS codes) is the class of [[4g + 2, 4 g, 2]] color codes derived from the tiling of the 4g-gon by the regular {4g + 2, 3} tessellation. Such codes are obtained from the {4 g, 4g} tessellation whose Fuchsian group associated with the fundamental region consists of opposite edge-pairing transformations as the planar model of an arbitrary compact orientable surface of genus g. (C) 2022 Elsevier B.V. All rights reserved.

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页数：7

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