On simple radical difference families
On simple radical difference families
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DOI：
10.1002/jcd.3180030208
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发表时间：
1995
影响因子：
0.7
通讯作者：
M. Buratti
中科院分区：
文献类型：
--
作者：
M. Buratti
对于q是一个素数幂，k是奇（偶）数，我们定义一个（q，k，1）差族是根，如果每个基块是GF（q）乘法群中单位的k次根的陪集（GF（q）乘法群中单位的第（k − 1）次根的陪集与零的并）。这样的族将由RDF表示。关于这个问题的主要结果是1972年R.M. Wilson;它是对任意k存在（q，k，1）-RDF的充分条件。我们改进了这个结果，用另一个充分但较弱的条件代替Wilson条件，证明了至少对k ≤ 7是必要的。因此，我们得到新的差族，从而新的Steiner 2-设计。John Wiley & Sons，Inc.
For q a prime power and k odd (even), we define a (q,k,1) difference family to be radical if each base block is a coset of the kth roots of unity in the multiplicative group of GF(q) (the union of a coset of the (k − 1)th roots of unity in the multiplicative group of GF(q) with zero). Such a family will be denoted by RDF. The main result on this subject is a theorem dated 1972 by R.M. Wilson; it is a sufficient condition for the existence of a (q,k, 1)-RDF for any k. We improve this result by replacing Wilson's condition with another sufficient but weaker condition, which is proved to be necessary at least for k ⩽ 7. As a consequence, we get new difference families and hence new Steiner 2-designs. © 1995 John Wiley & Sons, Inc.