Abstract
We introduce a uniform technique for constructing a family of symmetric designs with parameters (v(q m+1-1)/(q-1), kq m,λq m), where m is any positive integer, (v, k, λ) are parameters of an abelian difference set, and q = k 2/(k - λ) is a prime power. We utilize the Davis and Jedwab approach to constructing difference sets to show that our construction works whenever (v, k, λ) are parameters of a McFarland difference set or its complement, a Spence difference set or its complement, a Davis–Jedwab difference set or its complement, or a Hadamard difference set of order 9 · 4d, thus obtaining seven infinite families of symmetric designs.
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Ionin, Y.J. Building Symmetric Designs With Building Sets. Designs, Codes and Cryptography 17, 159–175 (1999). https://doi.org/10.1023/A:1026465125305
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DOI: https://doi.org/10.1023/A:1026465125305