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arXiv · 1505.04611

A Generalization of Combinatorial Designs Related to Almost Difference Sets

Jerod Michel·Baokun Ding
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Abstract

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.

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Jerod Michel, Baokun Ding. 2015-05-18. A Generalization of Combinatorial Designs Related to Almost Difference Sets. https://arxiv.org/abs/1505.04611

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