  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.
