Problems of Information Transmission

, Volume 46, Issue 4, pp 321–345 | Cite as

Special sequences as subcodes of reed-solomon codes

  • A. A. DavydovEmail author
  • V. V. Zyablov
  • R. E. Kalimullin
Coding Theory


We consider sequences in which every symbol of an alphabet occurs at most once. We construct families of such sequences as nonlinear subcodes of a q-ary [n, k, n − k + 1] q Reed-Solomon code of length nq consisting of words that have no identical symbols. We introduce the notion of a bunch of words of a linear code. For dimensions k ≤ 3 we obtain constructive lower estimates (tight bounds in a number of cases) on the maximum cardinality of a subcode for various n and q, and construct subsets of words meeting these estimates and bounds. We define codes with words that have no identical symbols, observe their relation to permutation codes, and state an optimization problem for them.


Generator Matrix Information Transmission Linear Code Generator Matrice Base Polynomial 
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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. A. Davydov
    • 1
    Email author
  • V. V. Zyablov
    • 1
  • R. E. Kalimullin
    • 1
  1. 1.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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