Constructions for Permutation Codes in Powerline Communications

  • Authors:

  • Wensong Chu;Charles J. Colbourn;Peter Dukes

  • Affiliations:

  • Department of Computer Science and Engineering, Arizona State University, Tempe, AZ 85287-8809, U.S.A. wensong.chu@asu.edu;Department of Computer Science and Engineering, Arizona State University, Tempe, AZ 85287-8809, U.S.A. colbourn@asu.edu;Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 1A1 dukes@math.toronto.edu

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2004

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Abstract

A permutation array (or code) of length n and distance d is a set Γ of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x, y ∈ Γ is at least d. One motivation for coding with permutations is powerline communication. After summarizing known results, it is shown here that certain families of polynomials over finite fields give rise to permutation arrays. Additionally, several new computational constructions are given, often making use of automorphism groups. Finally, a recursive construction for permutation arrays is presented, using and motivating the more general notion of codes with constant weight composition.