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Designs, Codes and Cryptography

, Volume 48, Issue 2, pp 141–154 | Cite as

Binary permutation sequences as subsets of Levenshtein codes, spectral null codes, run-length limited codes and constant weight codes

  • Khmaies Ouahada
  • Theo G. Swart
  • Hendrik C. Ferreira
  • Ling Cheng
Article

Abstract

We investigate binary sequences which can be obtained by concatenating the columns of (0,1)-matrices derived from permutation sequences. We then prove that these binary sequences are subsets of a surprisingly diverse ensemble of codes, namely the Levenshtein codes, capable of correcting insertion/deletion errors; spectral null codes, with spectral nulls at certain frequencies; as well as being subsets of run-length limited codes, Nyquist null codes and constant weight codes.

Keywords

Permutation codes Insertion/deletion correcting codes Constant weight codes Spectral null codes Run-length limited codes 

AMS Classifications

20B30 20B35 68P30 94A05 94A24 94B50 94B60 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Khmaies Ouahada
    • 1
  • Theo G. Swart
    • 1
  • Hendrik C. Ferreira
    • 1
  • Ling Cheng
    • 1
  1. 1.Department of Electrical and Electronic Engineering ScienceUniversity of JohannesburgAuckland ParkSouth Africa

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