Cyclotomic difference sets in finite fields
Combinatorics
2017-07-05 v3
Abstract
The classical problem of whether th-powers with or without zero in a finite field form a difference set has been extensively studied, and is related to many topics, such as flag transitive finite projective planes. In this paper new necessary and sufficient conditions are established including those via a system of polynomial equations on Gauss sums. The author thereby solves the problem for even which is neglected in the literature, and extends the nonexistence list for even up to . Moreover, conjectures toward the complete classification are posed.
Cite
@article{arxiv.1501.03275,
title = {Cyclotomic difference sets in finite fields},
author = {Binzhou Xia},
journal= {arXiv preprint arXiv:1501.03275},
year = {2017}
}