On the construction of perfect codes from HEX signal constellations
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Pergamon-Elsevier B.V. Ltd
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Abstract
Recently, minimum and non-minimum delay perfect codes were proposed for any channel of dimension n. Their construction appears in the literature as a subset of cyclic division algebras over Q(zeta(3)) only for the dimension n = 2(s)n(1), where s is an element of {0,1}, n(1) is odd and the signal constellations are isomorphic to Z[zeta(3)](n) In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over Q(zeta(3)), where the signal constellations are isomorphic to the hexagonal A(2)(n)-rotated lattice, for any channel of any dimension n such that gcd(n,3) = 1. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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Journal of The Franklin Institute-engineering and Applied Mathematics. Oxford: Pergamon-Elsevier B.V. Ltd, v. 349, n. 10, p. 3060-3077, 2012.
