# Salem sets in vector spaces over finite fields

## TL;DR

This paper demonstrates that most random subsets of finite vector spaces have small Fourier coefficients, classifying them as weak Salem sets, and extends previous results to a new probabilistic context.

## Contribution

It extends Hayes's result by showing that almost all random subsets in finite vector spaces are weak Salem sets under a different probability model.

## Key findings

- Most random subsets are weak Salem sets
- Extension of Hayes's result to a new model
- Small Fourier coefficients in the majority of cases

## Abstract

We prove that almost all random subsets of a finite vector space are weak Salem sets (small Fourier coefficient), which extends a result of Hayes to a different probability model.