Metrics which turn tilings into binary perfect codes

Gabriella Akemi Miyamoto; Marcelo Firer

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arXiv · 1903.05951

Metrics which turn tilings into binary perfect codes

Gabriella Akemi Miyamoto·Marcelo Firer

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Abstract

In this work, we consider tilings of the Hamming cube and look for metrics which turn the tilings into a perfect code. We consider the family of metrics which are determined by a weight and are compatible with the support of vectors (TS-metrics). We determine which of the tilings with small tiles or high rank can be a perfect code for some TS-metric and we characterize all such metrics. Finally, we show some procedures to obtain new perfect codes (relatively to TS-metrics) out of existing ones.

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Gabriella Akemi Miyamoto, Marcelo Firer. 2019-03-14. Metrics which turn tilings into binary perfect codes. https://arxiv.org/abs/1903.05951

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