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