Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal integral point sets in affine planes over finite fields   Motivated by integral point sets in the Euclidean plane, we consider integral
point sets in affine planes over finite fields. An integral point set is a set
of points in the affine plane $\mathbb{F}_q^2$ over a finite field
$\mathbb{F}_q$, where the formally defined squared Euclidean distance of every
pair of points is a square in $\mathbb{F}_q$. It turns out that integral point
sets over $\mathbb{F}_q$ can also be characterized as affine point sets
determining certain prescribed directions, which gives a relation to the work
of Blokhuis. Furthermore, in one important sub-case integral point sets can be
restated as cliques in Paley graphs of square order. In this article we give
new results on the automorphisms of integral point sets and classify maximal
integral point sets over $\mathbb{F}_q$ for $q\le 47$. Furthermore, we give two
series of maximal integral point sets and prove their maximality.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga