Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

A new table of permutation codes

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

Permutation codes (or permutation arrays) have received considerable interest in recent years, partly motivated by a potential application to powerline communication. Powerline communication is the transmission of data over the electricity distribution system. This environment is rather hostile to communication and the requirements are such that permutation codes may be suitable. The problem addressed in this study is the construction of permutation codes with a specified length and minimum Hamming distance, and with as many codewords (permutations) as possible. A number of techniques are used including construction by automorphism group and several variations of clique search based on vertex degrees. Many significant improvements are obtained to the size of the best known codes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bailey R.F.: Error-correcting codes from permutation groups. Discrete Math. 309, 4253–4265 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blake I.F.: Permutation codes for discrete channels. IEEE Trans. Inform. Theory 20(1), 138–140 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bogaerts M.: New upper bounds for the size of permutation codes via linear programming. Electron. J. Combi. 17(#R135) (2010).

  4. Burer S., Monteiro R.D.C., Zhang Y.: Maximum stable set formulations and heuristics based on continuous optimization. Math. Progr. Ser A. 94, 137–166 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cannon J.J., Bosma W. (eds.): Handbook of magma functions, version 2.13. The University of Sydney, Sydney (2006).

  6. Carraghan R., Pardalos P.M.: An exact algorithm for the maximum clique problem. Oper. Res. Lett. 9, 375–382 (1990)

    Article  MATH  Google Scholar 

  7. Chu W., Colbourn C.J., Dukes P.: Constructions for permutation codes in powerline communications. Des., Codes Cryptogr. 32, 51–64 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Colbourn C.J., Kløve T., Ling A.C.H.: Permutation arrays for powerline communication and mutually orthogonal latin squares. IEEE Trans. Inform. Theory 50, 1289–1291 (2004)

    Article  MathSciNet  Google Scholar 

  9. Deza M., Vanstone S.A.: Bounds for permutation arrays. J. Statist. Plann. Inference 2, 197–209 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dukes P., Sawchuck N.: Bounds on permutation codes of distance four. J. Algebr. Comb. 31, 143–158 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Frankl P., Deza M.: On maximal numbers of permutations with given maximal or minimal distance. J. Combin. Theory Ser. A 22, 352–360 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  12. Han Vinck A.J.: Coded modulation for power line communications. A.E.Ü. Int. J. Electron. Commun. 54(1), 45–49 (2000)

    Google Scholar 

  13. Huczynska S.: Powerline communications and the 36 officers problem. Phil. Trans. R. Soc. A. 364, 3199–3214 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hulpke A.: Constructing transitive permutation groups. J. Symbolic Comput. 39(1), 1–30 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Hurley S., Smith D.H., Thiel S.U.: FASoft: A system for discrete channel frequency assignment. Radio Sci. 32(5), 1921–1939 (1997)

    Article  Google Scholar 

  16. Janiszczak I., Staszewski R.: An improved bound for permutation arrays of length 10. http://www.iem.uni-due.de/preprints/IJRS.pdf (downloaded 1st March 2011).

  17. Konc J., Janežič D.: An improved branch and bound algorithm for the maximum clique problem. MATCH communications in mathematical and in computer chemistry 58, 569–590 (2007)

    MathSciNet  Google Scholar 

  18. Montemanni R., Smith D.H.: Heuristic algorithms for constructing binary constant weight codes. IEEE Trans. Inform. Theory 55(10), 4651–4656 (2009)

    Article  MathSciNet  Google Scholar 

  19. Östergård P.R.J.: A new algorithm for the maximum-weight clique problem. Nordic J. Comput. 8(4), 424–436 (2001)

    MATH  MathSciNet  Google Scholar 

  20. Östergård P.R.J.: A fast algorithm for the maximum clique problem. Dis. Appl. Math. 120, 197–207 (2002)

    Article  MATH  Google Scholar 

  21. Pavlidou N., Han Vinck A.J., Yazdani J., Honary B.: Power line communications: state of the art and future trends. IEEE Commun. Mag. 41(4), 34–40 (2003)

    Article  Google Scholar 

  22. Tarnanen H.: Upper bounds on permutation codes via linear programming. Eur. J. Combin. 20, 101–114 (1999)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Mathematics and Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales, UK

    Derek H. Smith

  2. Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Galleria 2, 6928, Manno, Switzerland

    Roberto Montemanni

Authors
  1. Derek H. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Montemanni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roberto Montemanni.

Additional information

Communicated by C. J. Colbourn.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, D.H., Montemanni, R. A new table of permutation codes. Des. Codes Cryptogr. 63, 241–253 (2012). https://doi.org/10.1007/s10623-011-9551-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-011-9551-8

Keywords

Mathematics Subject Classification (2000)

Search

Navigation