  In this work we explore a family of metrics over finite fields which respect
the support of vectors. We show how these metrics can be obtained from the
edge-weighted Hamming cube and, based on this representation we give a
description of a group of linear isometries (with respect to the metric). Next
we introduce the concept of conditional sum of metrics and determine what
conditions determine a metric respecting support, out of two such given
metrics. Finally we introduce the labeled-poset block metrics, a new family of
metrics which respects support of vector, filling a gap existing in the known
such metrics. For this family we give a full description of the group of linear
isometries and determine necessary and sufficient conditions for the existence
of a MacWilliams identity.
