Title: Classes of permutation arrays in finite projective spaces
Author: T.L. Alderson, Keith E. Mellinger
Department of Mathematics, University of New Brunswick, Saint John, NB E2L 4L5, Canada.
Department of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, Fredericksburg, VA 22401, USA
Abstract: 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.
Keywords: permutation arrays; finite projective spaces; spreads; nonlinear codes.
Int. J. of Information and Coding Theory, 2010 Vol.1, No.4, pp.371 - 383
Available online: 25 Apr 2010