On MDS color codes

Clarice Dias de Albuquerque, Vandenberg Lopes Vieira, Cátia Regina de Oliveira Quilles Queiroz, Giuliano Gadioli La Guardia, Anderson José de Oliveira and Leandro Bezerra de Lima

Physica A: Statistical Mechanics and its Applications, 2022, vol. 599, issue C

Abstract: 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+2,4g,2]] color codes derived from the tiling of the 4g-gon by the regular {4g+2,3} tessellation. Such codes are obtained from the {4g,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.

Keywords: Topological codes; Surface codes; Quantum codes (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:599:y:2022:i:c:s0378437122003193

DOI: 10.1016/j.physa.2022.127433

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