Skip to main content
Springer Nature Link
Log in

Enumeration, Construction and Random Generation of Block Codes

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

Abstract

We discuss some methods for the enumeration, construction and random generation of isometry classes of block codes using methods from algebraic combinatorics.

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. C.J. Colbourn and R.C. Read, Orderly algorithms for generating restricted classes of graphs, Journal of Graph Theory, Vol. 3 (1979) pp. 187 - 195.

    Google Scholar 

  2. J.D. Dixon and H.S. Wilf, The random selection of unlabeled graphs, Journal of Algorithms, Vol. 4 (1983) pp. 205 - 213.

    Google Scholar 

  3. H. Fripertinger, Enumeration of isometry classes of linear (n, k)-codes over GF(q) in SYMMETRICA, Bayreuther Mathematische Schriften, Vol. 49 (1995) pp. 215 - 223.

    Google Scholar 

  4. H. Fripertinger, Zyklenzeiger linearer Gruppen und Abzählung linearer Codes, Séminaire Lotharingien de Combinatoire, Vol. 33 (1995) pp. 1 - 10.

    Google Scholar 

  5. H. Fripertinger, Enumeration of Linear Codes by Applying Methods from Algebraic Combinatorics, Grazer Math. Berichte, Vol. 328 (1996) pp. 31 - 42.

    Google Scholar 

  6. H. Fripertinger and A. Kerber, Isometry Classes of Indecomposable Linear Codes, In G. Cohen, M. Giusti, and T. Mora, editors, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 11th International Symposium, AAECC-11, Paris, France, July 1995, volume 948 of Lecture Notes in Computer Science, Springer (1995) pp. 194–204.

  7. R. Grund, Symmetrieklassen von Abbildungen und die Konstruktion von diskreten Strukturen, Bayreuther Mathematische Schriften, Vol. 31 (1990) pp. 19 - 54.

    Google Scholar 

  8. M.A. Harrison, Counting Theorems and their Applications to Switching Theory, In A. Mukhopadyay, editor, Recent Developments in Switching Functions, chapter 4, Academic Press (1971) pp. 85 - 120.

  9. M.A. Harrison and R.G. High, On the Cycle Index of a Product of Permutation Groups, Journal of Combinatorial Theory, Vol. 4 (1968) pp. 277 - 299.

    Google Scholar 

  10. A. Kerber, Anwendungsorientierte Theorie endlicher Strukturen, To be published.

  11. A. Kerber, Der Zykelindex der Exponentialgruppe, Mitteilungen aus dem Mathematischen Seminar Giessen, Vol. 98 (1973) pp. 5 - 20.

    Google Scholar 

  12. A. Kerber, Algebraic Combinatorics via Finite Group Actions, B.I.Wissenschaftsverlag, Mannheim,Wien, Zürich (1991).

    Google Scholar 

  13. A. Kerber, Algebraic Combinatorics in Bayreuth, Séminaire Lotharingien de Combinatoire, B34j (1995). http://cartan.u-strasbg.fr/ slc//divers/../wpapers/s34bayreuth.html.

  14. H. Lehmann, Das Abzähltheorem der Exponentialgruppe in gewichteter Form, Mitteilungen aus dem Mathem. Seminar Giessen, Vol. 112 (1974) pp. 19 - 33.

    Google Scholar 

  15. H. Lehmann, Ein vereinheitlichender Ansatz für die REDFIELD-PÓLYA- de BRUIJNSCHE Abzähltheorie, PhD thesis, Universität Giessen (1976).

  16. E.M. Palmer and R.W. Robinson, Enumeration under two representations of the wreath product, Acta Mathematica, Vol. 131 (1973) pp. 123 - 143.

    Google Scholar 

  17. E.M. Palmer and Robinson R.W., The matrix group of two permutation groups, Bull. Amer. Math. Soc., Vol. 73 (1967) pp. 204 - 207.

    Google Scholar 

  18. G. Pólya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Mathematica, Vol. 68 (1937) pp. 145 - 254.

    Google Scholar 

  19. R.C. Read, Every one a winner, Ann. Discrete Mathematics, Vol. 2 (1978) pp. 107 - 120.

    Google Scholar 

  20. C.C. Sims, Computational methods in the study of permutation groups, Computational Problems in Abstract Algebra, (1970) pp. 169 - 183.

  21. D. Slepian, On the Number of Symmetry Types of Boolean Functions of nVariables, Canad. J. Math., Vol. 5 (1953) pp. 185 - 193.

    Google Scholar 

  22. SYMMETRICA, A program system devoted to representation theory, invariant theory and combinatorics of finite symmetric groups and related classes of groups, Copyright by ”Lehrstuhl II für Mathematik, Universität Bayreuth, 95440 Bayreuth,” Distributed via anonymous ftp 132.180.16.20 in dist/SYM.tar.Z.

Download references

Author information

Authors and Affiliations

  1. Institut füur Mathematik, Karl-Franzens-Universität Graz, Heinrichstraße 36, A-8010 Graz

    Harald Fripertinger

Authors
  1. Harald Fripertinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fripertinger, H. Enumeration, Construction and Random Generation of Block Codes. Designs, Codes and Cryptography 14, 213–219 (1998). https://doi.org/10.1023/A:1008248618779

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008248618779

Search

Navigation