On the number of orthogonal systems in vector spaces over finite fields

TL;DR

This paper provides a graph theoretic proof that large enough subsets of finite field vector spaces contain many mutually orthogonal k-tuples, extending understanding of orthogonal systems in finite fields.

Contribution

It introduces a novel graph theoretic approach to establish the abundance of orthogonal k-tuples in large subsets of finite field vector spaces.

Findings

Large subsets contain many orthogonal k-tuples

Graph theoretic proof method

Extension of previous results

Abstract

Iosevich and Senger (2008) showed that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors. In this note, we provide a graph theoretic proof of this result.