Classifying Equidistant Permutation Codes

ABSTRACT A permutation code of length is a set of codewords, each of which contains every symbol of a set of size exactly once. A permutation code in which any two distinct codewords differ in the same number of coordinates is called equidistant and that number is called the distance. The maximum size of an equidistant permutation code of length and distance is denoted by . An algorithm for classifying equidistant permutation codes is here presented and is in particular used to show that with 12 optimal codes up to isometry. Ingredients of the algorithm include a classification of Latin rectangles, a tailored algorithm for finding cliques in graphs, and validation by double counting.