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Binary ( k , k )-Designs

Author

Listed:
  • Todorka Alexandrova

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113 Sofia, Bulgaria)

  • Peter Boyvalenkov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113 Sofia, Bulgaria)

  • Angel Dimitrov

    (Department of Mathematics, Technical University Munich, Boltzmannstrasse 3, Garching b. 85748 Munich, Germany)

Abstract

We introduce and investigate binary ( k , k ) -designs, a special case of T -designs. Our combinatorial interpretation relates ( k , k ) -designs to the binary orthogonal arrays. We derive a general linear programming bound and propose as a consequence a universal bound on the minimum possible cardinality of ( k , k ) -designs for fixed k and n . Designs which attain our bound are investigated.

Suggested Citation

  • Todorka Alexandrova & Peter Boyvalenkov & Angel Dimitrov, 2020. "Binary ( k , k )-Designs," Mathematics, MDPI, vol. 8(11), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1883-:d:437444
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