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

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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.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering Science, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa

    Khmaies Ouahada, Theo G. Swart, Hendrik C. Ferreira & Ling Cheng

Authors
  1. Khmaies Ouahada
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  2. Theo G. Swart
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  3. Hendrik C. Ferreira
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  4. Ling Cheng
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Corresponding author

Correspondence to Hendrik C. Ferreira.

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Ouahada, K., Swart, T.G., Ferreira, H.C. et al. Binary permutation sequences as subsets of Levenshtein codes, spectral null codes, run-length limited codes and constant weight codes. Des. Codes Cryptogr. 48, 141–154 (2008). https://doi.org/10.1007/s10623-007-9161-7

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  • DOI: https://doi.org/10.1007/s10623-007-9161-7

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