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

TL;DR

This paper introduces a reduction technique for mixed integer programming models of mixed Hamming packings, leading to improved upper bounds and more efficient solutions for maximal code cardinality problems.

Contribution

The paper presents a novel reduction method for MILP models of mixed Hamming packings, enhancing computational efficiency and improving known upper bounds.

Findings

Several best known upper bounds are improved.

Some bounds are proven to be sharp.

The reduction technique enables more efficient solutions.

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.