Designs, Codes and Cryptography

, Volume 41, Issue 1, pp 79–86 | Cite as

A random construction for permutation codes and the covering radius

  • Peter Keevash
  • Cheng Yeaw Ku


We analyse a probabilistic argument that gives a semi-random construction for a permutation code on n symbols with distance n − s and size Θ(s!(log n)1/2), and a bound on the covering radius for sets of permutations in terms of a certain frequency parameter.


Permutation codes Covering radius Restricted intersections 

AMS Classification



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  1. 1.
    Alon, N, Spencer, J 2000The probabilistic method2Wiley-Interscience [John Wiley & Sons]New YorkMATHCrossRefGoogle Scholar
  2. 2.
    Babai L, Frankl P (1992) Linear algebra methods in combinatorics. Department of Computer Science, University of Chicago, Preliminary versionGoogle Scholar
  3. 3.
    Cameron, PJ, Ku, CY 2003Intersecting families of permutationsEuro J Combin24881890MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Cameron, PJ, Wanless, IM 2005Covering radius for sets of permutationsDisc Math29391109MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Chu, W, Colbourn, CJ, Dukes, P 2004Constructions for permutation codes in powerline communicationsDes Codes Cryptogr325164MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Deza, M, Mrankl, P 1977On the maximum number of permutations with given maximal or minimal distanceJ Combin Theory Ser A22352360CrossRefGoogle Scholar
  7. 7.
    Ding, C, Fu, F-W, Klve, T, Wei, VK-W 2002Constructions of permutation arraysIEEE Trans Inform Theory48977980MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Erdős, P, Ko, C, Rado, R 1961Intersection theorems for systems of finite setsQuart J Math Oxford Ser12313320MathSciNetGoogle Scholar
  9. 9.
    Erdős, P, Spencer, J 1991Lopsided Lovász local lemma and Latin transversalsDisc Appl Math30151154CrossRefGoogle Scholar
  10. 10.
    Frankl, P 1995Extremal set systemsGraham, RLGrotschel, MLovasz, L eds. Handbook of combinatoricsElsevierAmsterdam12931329Google Scholar
  11. 11.
    Fu, F-W, Kløve, T 2004Two constructions of permutation arraysIEEE Trans Inform Theory50881883MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kézdy AE, Snevily HS, unpublished manuscriptGoogle Scholar
  13. 13.
    MacWilliams, FJ, Sloane, NJA 1977The theory of error-correcting codesNorth-HollandAmsterdamMATHGoogle Scholar
  14. 14.
    Pavlidou, N, Vinck, AJH, Yazdani, J, Honary, B 2003Power line communications: state of the art and future trendsIEEE Commun Mag413440CrossRefGoogle Scholar
  15. 15.
    Tarnanen, H 1999Upper bounds on permutation codes via linear programmingEuro J Combin20101114MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of MathematicsCaltech, PasadenaUSA

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