Canonical form of linear subspaces and coding invariants: the poset metric point of view

Abstract

In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of maximal decompositions according to the metric. These decompositions turns to be an important tool to obtain the canonical form for codes over any poset metrics and to obtain bounds for important invariants such as the packing radius of a linear subspace. Furthermore, using maximal decompositions, we are able to reduce and optimize the full lookup table algorithm for the syndrome decoding process.