On the construction of perfect codes from HEX signal constellations

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(ζ3) only for the dimension n=2sn1, where s∈{0,1}, n1 is odd and the signal constellations are isomorphic to Z[ζ3]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(ζ3), where the signal constellations are isomorphic to the hexagonal A2n-rotated lattice, for any channel of any dimension n such that gcd(n,3)=1.

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