2005
DOI: 10.1590/s0101-82052005000200002
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Geometrically uniform hyperbolic codes

Abstract: Abstract. In this paper we generalize the concept of geometrically uniform codes, formerly employed in Euclidean spaces, to hyperbolic spaces. We also show a characterization of generalized coset codes through the concept of G-linear codes.Mathematical subject classification: 14L35, 94B60.

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Cited by 13 publications
(11 citation statements)
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“…In this section, some basic and important concepts regarding geometrically uniform signal sets, quaternion algebras, quaternion orders, and arithmetic Fuchsian groups for this paper's development are presented. For a detailed description of these concepts we refer the reader to [1], [2] and [16]- [22].…”
Section: Preliminariesmentioning
confidence: 99%
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“…In this section, some basic and important concepts regarding geometrically uniform signal sets, quaternion algebras, quaternion orders, and arithmetic Fuchsian groups for this paper's development are presented. For a detailed description of these concepts we refer the reader to [1], [2] and [16]- [22].…”
Section: Preliminariesmentioning
confidence: 99%
“…), in the Euclidean sense. Theorem 2.1: [2] If S is a geometrically uniform signal set, then all the Dirichlet regions have the same shape.…”
Section: A Geometrically Uniform Signal Setsmentioning
confidence: 99%
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“…The main potential for coding in the hyperbolic plane is the infinitude of essentially distinct tessellations, in contrast to a Euclidean case. After [1], several papers connecting hyperbolic geometry with communication and coding theory have been published, [2], [3], [4], [5], among others. In [6] it is stated that it is possible to devise more efficient error correcting codes, in terms of error probability, if they are elaborated from two-dimensional varieties with genus g ≥ 2.…”
Section: Introductionmentioning
confidence: 99%