Permutation codes via fragmentation of group orbits

This work presents an approach to the Maximum Permutation Code Problem (MPCP) that exploits the orbits of permutation groups in a new way. Several scientific works of recent years studied the principle of building feasible codes by combining the orbits of single permutation groups. However, the idea of combining orbits stemming from more than one group has not been explored yet. This paper presents some experiments and results with a multi-group approach. Furthermore, it explores the potential of using subsets of orbits (fragments) instead of entire orbits. The concept of minimum distance code is introduced and studied in the special case of the orbits of cyclic groups. Computational experiments carried out with a branch and bound algorithm show the potential of this approach to obtain new lower bounds on open MPCP problems.