Distance-preserving and distance-increasing mappings from ternary vectors to permutations

Jyh Shyan Lin*, Jen Chun Chang, Rong-Jaye Chen, Torleiv Kløve

*Corresponding author for this work

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

Permutation arrays have found applications in powerline communication. One construction method for permutation arrays is to map good codes to permutations using a distance-preserving mappings (DPM). DPMs are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of some fixed length (the same or longer) such that every two distinct vectors are mapped to permutations with the same or larger Hamming distance than that of the vectors. A DPM is called distance increasing (DIM) if the distances are strictly increased (except when the two vectors are equal). In this correspondence, we propose constructions of DPMs and DIMs from ternary vectors. The constructed DPMs and DIMs improve many lower bounds on the maximal size of permutation arrays.

Original languageEnglish
Pages (from-to)1334-1339
Number of pages6
JournalIEEE Transactions on Information Theory
Volume54
Issue number3
DOIs
StatePublished - 1 Mar 2008

Keywords

  • Distance-increasing mappings
  • Distance-preserving mappings
  • Permutation arrays
  • Powerline communication

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