Jerod Michel, Baokun Ding
Published 2015-05-18Version 1
In this paper we study a certain generalization of combinatorial designs related to almost difference sets, namely the $t$-adesign, which was coined by Cunsheng Ding in 2015. It is clear that $2$-adesigns are a kind of partially balanced incomplete block design which naturally arise in many combinatorial and statistical problems. We discuss some of their basic properties and give several constructions of $2$-adesigns (some of which correspond to new almost difference sets, and others of which correspond to new almost difference families), as well as two constructions of $3$-adesigns. We also discuss some basic properties of their incidence matrices and codes.
A generalization of Croot-Lev -Pach's Lemma and a new upper bound for the size of difference sets in polynomial rings
Small examples of mosaics of combinatorial designs
On abelian $(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m)$-difference sets
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