Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness

Details Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness

2008-04-18

arxiv.org/abs/0804.3036v1

Mathematics

Combinatorics

Scientific paper

In this paper we systematically study various properties of the distance
graph in ${\Bbb F}_q^d$, the $d$-dimensional vector space over the finite field
${\Bbb F}_q$ with $q$ elements. In the process we compute the diameter of
distance graphs and show that sufficiently large subsets of $d$-dimensional
vector spaces over finite fields contain every possible finite configurations.

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