A lower bound on permutation codes of distance $n-1$

Abstract

A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length n and minimum distance n − 1. When such codes of length p + 1 are included as ingredients, we obtain a general lower bound M (n, n − 1) ≥ n 1.0797 for large n, gaining a small improvement on the guarantee given from MOLS.