Designs, Codes and Cryptography

, Volume 2, Issue 2, pp 189–206

Quasi-symmetric designs and the Smith Normal Form

  • A. Blokhuis
  • A. R. Calderbank

DOI: 10.1007/BF00124897

Cite this article as:
Blokhuis, A. & Calderbank, A.R. Des Codes Crypt (1992) 2: 189. doi:10.1007/BF00124897


We obtain necessary conditions for the existence of a 2 − (ν, k, λ) design, for which the block intersection sizes s1, s2, ..., snsatisfy s1s2 ≡ ... ≡ sns (mod pe),where p is a prime and the exponent e is odd. These conditions are obtained from restriction on the Smith Normal Form of the incidence matrix of the design. We also obtain restrictions on the action of the automorphism group of a 2 − (ν, k, λ) design on points and on blocks.

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • A. Blokhuis
    • 1
  • A. R. Calderbank
    • 2
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Mathematical Sciences Research Center, AT&T Bell LaboratoriesMurray HillUSA

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