Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Designs over finite fields by difference methods   One of the very first results about designs over finite fields, by S. Thomas,
is the existence of a cyclic 2-$(n,3,7)$ design over $\mathbb{F}_{2}$ for every
integer $n$ coprime with 6. Here, by means of difference methods, we reprove
and improve a little bit this result showing that it is true, more generally,
for every odd $n$. In this way, we also find the first infinite family of
non-trivial cyclic group divisible designs over $\mathbb{F}_{2}$.

8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph