The equivalence of certain equidistant binary codes and symmetric bibds

Abstract

We study equidistant codes of length 4k + 1 having (constant) weight 2k, and (constant) distance 2k between codewords. The maximum number of codewords is 4k; this can be attained if and only ifk = (u 2 +u)/2 (for some integeru) and there exists a ((2u 2 + 2u + 1,u 2, (u 2u)/2) — SBIBD. Also, one can construct such a code, with 4k − 1 codewords, from a (4k − 1, 2k − 1,k − 1) — SBIBD.

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

References

  1. [1]

    W. G. Bridges, M. Hall, Jr., andJ. L. Hayden, Codes and designs,Journal of Comb. Theory A 31 (1981), 155–174.

    MATH  Article  MathSciNet  Google Scholar 

  2. [2]

    J. I. Hall, Bounds for equidistant codes and partial projective planes,Disc. Math. 17 (1977), 85–94.

    MATH  Article  Google Scholar 

  3. [3]

    M. Hall,Combinatorial Theory, Blaisdell, Waltham, Mass., 1967.

    Google Scholar 

  4. [4]

    R. C. Mullin, B. K. Roy, andP. J. Schellenberg, Isomorphic subgraphs having minimal intersections,J. Austral. Math. Soc. A, to appear.

  5. [5]

    S. A. Vanstone, A bound forv 0(r, λ),Proc. Fifth Southeastern Conference on combinatorics, graph theory, and computing, 661–673.

Download references

Author information

Affiliations

Authors

Additional information

Supported, in part by NSERC grants U0217 (D. R. Stinson), A3558 (G. H. J. van Rees).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Stinson, D.R., van Rees, G.H.J. The equivalence of certain equidistant binary codes and symmetric bibds. Combinatorica 4, 357–362 (1984). https://doi.org/10.1007/BF02579148

Download citation

AMS subject classification (1980)

  • 05 B 05