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 $$M(n,n-1) \ge n^{1.0797}$$ for large n, gaining a small improvement on the guarantee given from MOLS.