Quasi-symmetric designs and the Smith Normal Form
- Cite this article as:
- Blokhuis, A. & Calderbank, A.R. Des Codes Crypt (1992) 2: 189. doi:10.1007/BF00124897
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We obtain necessary conditions for the existence of a 2 − (ν, k, λ) design, for which the block intersection sizes s1, s2, ..., snsatisfy s1 ≡ s2 ≡ ... ≡ sn ≡ s (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.