Projections in vector spaces over finite fields
Changhao Chen
TL;DR
This paper investigates the properties of projections in vector spaces over finite fields, establishing bounds similar to Euclidean cases, and explores the behavior of projections for random and Fourier-decaying sets.
Contribution
It introduces finite field analogues of Euclidean projection bounds and analyzes projections of random and Fourier-decaying sets, providing new insights into finite field geometry.
Findings
Finite field analogues of Euclidean projection bounds established.
Examples of sets without exceptional projections constructed.
Projections of Fourier-decaying sets analyzed.
Abstract
We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional projections via projections of random sets. In the end we study the projections of sets which have the (discrete) Fourier decay.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical Dynamics and Fractals · Mathematical Approximation and Integration