Reduction and efficient solution of MILP models of mixed Hamming packings yielding improved upper bounds

Abstract

Mixed Hamming packings are considered: the maximal cardinality given a minimum codeword Hamming distance of mixed codes is addressed via mixed integer programming models. Adopting the concept of contact graph from classical continuous sphere packing problems, a reduction technique for the models is introduced, which enables their efficient solution. Several best known upper bounds are improved and some of them are found to be sharp.