Abstract
In this paper we present generalized edge-pairings for the family of hyperbolic tessellations $$\{10\lambda ,2\lambda \}$$ , with the purpose to obtain the corresponding discrete group of isometries. These tessellations have greater density packing than the self-dual tessellations $$\{4\lambda ,4\lambda \}$$ implying that the associated codes achieve the least error probability, or equivalently, that these codes are optimum codes.
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