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Journal of Information Science and Engineering, Vol. 23 No. 4, pp. 1227-1239 (July 2007)

New Constructions of Distance-Increasing Mappings and Permutation Arrays*

Jen-Chun Chang
 Department of Computer Science and Information Engineering
National Taipei University
Taipei, 237 Taiwan

Permutation arrays (PAs, or permutation codes) are useful in communication over power lines. Distance-increasing mappings (DIMs) from the set of binary vectors of a fixed length to the set of permutations of the same length that strictly increase Hamming distances (except when that is obviously not possible) are useful to construct permutation arrays. In this paper, we first give a new recursive construction of DIMs. Next, with a tricky and very different way to use the recursive construction of DIMs, we find a new construction of PAs. Finally, a new lower bound for the size of PAs is given.

Keywords: distance-preserving mappings (DPMs), distance-increasing mappings (DIMs), code constructions, permutation arrays (PAs), Hamming distance

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Received May 16, 2005; revised August 16 & October 24, 2005; accepted November 14, 2005.
Communicated by Chi-Jen Lu.
*This work was supported in part by the National Science Council of Taiwan, R.O.C., under contracts No. NSC 94-2213-E-305-003 and NSC 95-2213-E-305-002.