The packing radius of a code and partitioning problems: The case for poset metrics

Considering a poset metric as a generalization of Hamming´s metric, the packing radius of a code is not necessarily a function of the minimal distance. In this work we show, without any restriction on the poset, that the relation between the weight and the packing radius of a vector is equivalent to a generalization of the classical partition problem. We also generalize the well renown heuristic and deterministic algorithms of Karmakar-Karp and Korf, respectively, using an algebraic approach to the Differencing Method.