Orthogonal systems in vector spaces over finite fields

TL;DR

This paper proves that sufficiently large subsets of finite vector spaces contain many mutually orthogonal k-tuples, highlighting structural properties of such sets.

Contribution

It establishes a threshold size for subsets of finite vector spaces to guarantee the presence of numerous orthogonal k-tuples, advancing understanding of their combinatorial structure.

Findings

Large enough subsets contain many orthogonal k-tuples

Threshold size for orthogonality in finite vector spaces

Structural insights into finite field vector spaces

Abstract

We prove 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.