Modeling hexagonal constellations with Eisenstein-Jacobi graphs

Modeling hexagonal constellations with Eisenstein-Jacobi graphs A set of signal points is called a hexagonal constellation if it is possible to define a metric so that each point has exactly six neighbors at distance 1 from it. As sets of signal points, quotient rings of the ring of Eisenstein-Jacobi integers are considered. For each quotient ring, the corresponding graph is defined. In turn, the distance between two points of a quotient ring is defined as the corresponding graph distance. Under certain restrictions, a quotient ring is a hexagonal constellation with respect to this metric. For the considered hexagonal constellations, some classes of perfect codes are known. Using graphs leads to a new way of constructing these codes based on solving a standard graph-theoretic problem of finding a perfect dominating set. Also, a relation between the proposed metric and the well-known Lee metric is considered. Problems of Information Transmission Springer Journals

Modeling hexagonal constellations with Eisenstein-Jacobi graphs

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SP MAIK Nauka/Interperiodica
Copyright © 2008 by MAIK Nauka
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
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