Perfect codes in Euclidean lattices

Strey, Giselle; Strapasson, João E.; Costa, Sueli I. R.

doi:10.1007/s40314-021-01436-3

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2021

2024

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“…Besides the mathematical interest around tiling, including the estimation of Ramsey number of graphs [17], applications in coding theory are also well established. Connections between tilings and perfect codes were addressed in [2], for tilings of F n 2 with the Hamming metric and in [16], for tilings of general lattices by their sublattices with the Euclidean metric. Tilings of finite abelian groups were also explored in [13] in the context of public key cryptography.…”

Section: Introductionmentioning

confidence: 99%

Tiling of Constellations

Bollauf

Ytrehus

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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Motivated by applications in reliable and secure communication, we address the problem of tiling (or partitioning) a finite constellation in Z n 2 L by subsets, in the case that the constellation does not possess an abelian group structure. The property that we do require is that the constellation is generated by a linear code through an injective mapping. The intrinsic relation between the code and the constellation provides a sufficient condition for a tiling to exist. We also present a necessary condition. Inspired by a result in group theory, we discuss results on tiling for the particular case when the finer constellation is an abelian group as well.

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