Combinatorial t-designs from quadratic functions
Combinatorial t-designs from quadratic functions
复制标题
二次函数的组合 t 设计
DOI：
10.1007/s10623-019-00696-9
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Wang Qi
中科院分区：
文献类型：
--
作者：
Xiang Can;Ling Xin;Wang Qi
几十年来，组合t设计一直是组合学中一个有趣的话题。最近有报道称，某些特殊多项式的固定大小的象集可以构成t设计。到目前为止，关于利用特殊多项式构造t-设计的工作还很少，而且通常很难确定其参数。本文利用有限域上的二次函数进一步研究了这一思想，从而得到了无限族的2-设计，并显式地确定了它们的参数。得到的设计包括了一些早期的2-设计作为特例。此外，我们还证实了丁和唐(Arxiv：1903.07375,2019年)的猜想3。
Combinatorial t-designs have been an interesting topic in combinatorics for decades. It was recently reported that the image sets of a fixed size of certain special polynomials may constitute a t-design. Till now only a small amount of work on constructing t-designs from special polynomials has been done, and it is in general hard to determine their parameters. In this paper, we investigate this idea further by using quadratic functions over finite fields, thereby obtain infinite families of 2-designs, and explicitly determine their parameters. The obtained designs cover some earlier 2-designs as special cases. Furthermore, we confirm Conjecture 3 in Ding and Tang (ArXiv:1903.07375, 2019).