New upper bounds for the size of permutation codes via linear programming (Q612914)

Summary: An \((n,d)\)-permutation code of size \(s\) is a subset \(C\) of \(S_n\) with \(s\) elements such that the Hamming distance \(d_H\) between any two distinct elements of \(C\) is at least equal to \(d\). In this paper, we give new upper bounds for the maximal size \(\mu(n,d)\) of an \((n,d)\)-permutation code of degree \(n\) with \(11\leq n\leq 14\). In order to obtain these bounds, we use the structure of association scheme of the permutation group \(S_n\) and the irreducible characters of \(S_n\). The upper bounds for \(\mu(n,d)\) are determined solving an optimization problem with linear inequalities.