Classes of permutation arrays in finite projective spaces

摘要

We exhibit some techniques for constructing permutation arrays using projections in finite projective spaces and the geometry of arcs in the finite projective plane. We say a permutation array PA(n, d) has length n and minimum distance d when it consists of a collection of permutations on n symbols that pairwise agree in at most n - d coordinate positions. Such arrays can also be viewed as non-linear codes and are used in powerline communication. While our techniques likely do not produce optimal arrays, we are able to construct examples of codes for certain parameter sets for which no constructions were previously known.