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    NEW CLASSES OF TOPOLOGICAL QUANTUM CODES ASSOCIATED WITH SELF-DUAL, QUASI SELF-DUAL AND DENSER TESSELLATIONS

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    Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In this paper we present six classes of topological quantum codes (TQC) on compact surfaces with genus g >= 2. These codes are derived from self-dual, quasi self-dual and denser tessellations associated with embeddings of self-dual complete graphs and complete bipartite graphs on the corresponding compact surfaces. The majority of the new classes has the self-dual tessellations as their algebraic and geometric supporting mathematical structures. Every code achieves minimum distance 3 and its encoding rate is such that k/n -> 1as n -> infinity, except for the one case where k/n -> 1/3 as n -> infinity.1041984956970Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2007/56052-8, 2009/50837-9]CNPq [306617/2007-2, 305348/2009-4

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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