Isometry invariant permutation codes and mutually orthogonal Latin squares

Commonly, the direct construction and the description of mutually orthogonal Latin squares (MOLS) make use of difference or quasi-difference matrices. Now there exists a correspondence between MOLS and separable permutation codes. We present separable permutation codes of length 35, 48, 63, and 96 and minimum distance 34, 47, 62, and 95 consisting of 6 x 35, 10 x 48, 8 x 63, and 8 x 96 codewords, respectively. Using the correspondence, this gives 6 MOLS for n = 35, 10 MOLS for n = 48, 8 MOLS for n = 63, and 8 MOLS for n = 96. The codes are given by generators of an appropriate subgroup U of the isometry group of the symmetric group S-n and U-orbit representatives. This gives an alternative uniform way to describe the MOLS.