Building Symmetric Designs With Building Sets

Authors:
Yury J. Ionin
Affiliations:
Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA
Venue:
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Year:
1999

Citing 10
Cited 0

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Abstract

We introduce a uniformtechnique for constructing a family of symmetric designs withparameters (v(q^{m+1}-1)/(q-1),kq^m,\lambda q^m),where m is any positive integer, (v,k,\lambda) are parameters of an abelian difference set, and q=k^2/(k-\lambda) is a prime power. We utilize the Davis and Jedwab approachto constructing difference sets to show that our constructionworks whenever (v,k,\lambda ) are parameters ofa McFarland difference set or its complement, a Spence differenceset or its complement, a Davis–Jedwab difference set orits complement, or a Hadamard difference set of order 9\cdot4^d, thus obtaining seven infinite families of symmetricdesigns.