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Zbl 1231.94070
Costa, Sueli I. Rodrigues; Muniz, Marcelo; Agustini, Edson; Palazzo, Reginaldo
Graphs, tessellations, and perfect codes on flat tori. (English)
[J] IEEE Trans. Inf. Theory 50, No. 10, 2363-2377 (2004). ISSN 0018-9448

Summary: Quadrature amplitude modulation (QAM)-like signal sets are considered in this paper as coset constellations placed on regular graphs on surfaces known as flat tori. Such signal sets can be related to spherical, block, and trellis codes and may be viewed as geometrically uniform (GU) in the graph metric in a sense that extends the concept introduced by {\it G. D. Forney} jun. [IEEE Trans. Inf. Theory 37, No. 5, 1241--1260 (1991; Zbl 0734.94026)]. Homogeneous signal sets of any order can then be labeled by a cyclic group, induced by translations on the Euclidean plane. We construct classes of perfect codes on square graphs including Lee spaces, and on hexagonal and triangular graphs, all on flat tori. Extension of this approach to higher dimensions is also considered.

MSC 2000:: *94B15 Cyclic codes
94B27 Geometric methods in coding theory

Citations: Zbl 0734.94026

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