A branch and bound approach to permutation codes

The Maximum Permutation Code Problem (MPCP) is a well-known combinatorial optimization problem in coding theory. The aim is to generate the largest possible permutation codes, having a given length n and a minimum Hamming distance d between the codewords. In this paper we present a new branch and bound algorithm, which combines combinatorial techniques with an approach based on group orbits. Computational experiments lead to interesting considerations about the use of group orbits for code generation.