Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields

This is a preview of subscription content, access via your institution.

References

  1. [1]

    E. R. Berlekamp, J. H. van Lint andJ. J. Seidel, A strongly regular graph derived from the perfect ternary Golay code, in:A Survey of Combinatorial Theory (J. N. Srivastava, ed.), North-Holland, Amsterdam, 1973.

    Google Scholar 

  2. [2]

    R. C. Bose, Strongly regular graphs, partial geometries, and partially balanced designs,Pacific J. Math. 13 (1963) 389–419.

    MATH  MathSciNet  Google Scholar 

  3. [3]

    A. Cossu, Su alcune proprietà des {k;n}-archi di un piano proiettivo sopra un corpo finito,Rend. Mat. e Appl. 20 (1961) 271–277.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    P. Delsarte, Weights of linear codes and strongly regular normed spaces,Discrete Math. 3 (1972) 47–64.

    MATH  Article  MathSciNet  Google Scholar 

  5. [5]

    P. Delsarte, An algebraic approach to the association schemes of coding theory,Philips Res. Reports Suppl. 10 (1973).

  6. [6]

    J.-M. Goethals andJ. J. Seidel, The regular two-graph on 276 vertices,Discrete Math. 12 (1975) 143–158.

    MATH  Article  MathSciNet  Google Scholar 

  7. [7]

    R. E. Greenwood andA. M. Gleason, Combinatorial relations and chromatic graphs,Canad. J. Math. 7 (1955) 1–7.

    MATH  MathSciNet  Google Scholar 

  8. [8]

    X. L. Hubaut, Strongly regular graphs,Discrete Math. 13 (1975) 357–381.

    MATH  Article  MathSciNet  Google Scholar 

  9. [9]

    J. H. van Lint,Coding Theory,Lecture Notes in Math. 201, Springer, Berlin, 1971.

    Google Scholar 

  10. [10]

    D. M. Mesner, A new family of partially balanced incomplete block designs with some Latin square design properties,Ann. Math. Stat. 38 (1967) 571–581.

    MathSciNet  Google Scholar 

  11. [11]

    J. A. Thas, Combinatorics of partial geometries and generalized quadrangles, in:Higher Combinatorics (M. Aigner, ed.), Reidel, Dordrecht, 1977.

    Google Scholar 

  12. [12]

    H. C. A. van Tilborg, Uniformly packed codes,Thesis, Technological University Eindhoven, 1976.

  13. [13]

    W. D. Wallis, A. Street andJ. Wallis,Combinatorics: Room squares, Sum-Free Sets, Hadamard Matrices,Springer Lecture Notes in Math. 292, Springer, Berlin, 1972.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

The research of the second author was supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

van Lint, J.H., Schrijver, A. Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields. Combinatorica 1, 63–73 (1981). https://doi.org/10.1007/BF02579178

Download citation

AMS subject classification (1980)

  • 05 B 30
  • 05 B 25, 05 C 25