Obtaining binary perfect codes out of tilings

04/23/2019

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by   Gabriella Akemi Miyamoto, et al.

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A translation-support metric (TS-metric) is a metric which is translation-invariant and respects the support of vectors. We propose the use of tilings of the binary space to find new perfect codes (small and large) in TS-metrics. To do so, we use tilings already known in the literature and try to find some TS-metric in which the tile is a ball. We also propose the construction of new perfect codes obtained by the concatenation of two smaller ones.