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Quasi-symmetric designs and the Smith Normal Form

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Abstract

We obtain necessary conditions for the existence of a 2 − (ν, k, λ) design, for which the block intersection sizes s 1, s 2, ..., s n satisfy s 1 ≡ s 2 ≡ ... ≡ s n ≡ s (mod p e),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.

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    A. Blokhuis

  2. Mathematical Sciences Research Center, AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    A. R. Calderbank

Authors
  1. A. Blokhuis
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  2. A. R. Calderbank
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Communicated by V.D. Tonchev

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Blokhuis, A., Calderbank, A.R. Quasi-symmetric designs and the Smith Normal Form. Des Codes Crypt 2, 189–206 (1992). https://doi.org/10.1007/BF00124897

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  • DOI: https://doi.org/10.1007/BF00124897

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