Intersective sets over abelian groups
Abstract
Abstract Given a finite abelian group G and a subset $$J\subset G$$ J ⊂ G with $$0\in J$$ 0 ∈ J , let $$D_{G}(J,N)$$ D G ( J , N ) be the maximum size of $$A\subset G^{N}$$ A ⊂ G N such that the difference set $$A-A$$ A - A and $$J^{N}$$ J N have no non-trivial intersection. Recently, this extremal problem has been widely studied for different groups G and subsets J . In this paper, we generalize and improve the relevant results by Alon and by Hegedűs by building a bridge between this problem and cyclotomic polynomials with the help of algebraic graph theory. In particular, we construct infinitely many non-trivial families of G and J for which the current known upper bounds on $$D_{G}(J, N)$$ D G ( J , N ) can be improved exponentially.
Fields of Study & Subjects
graph theory and CDMA systems
Coding theory and cryptography
Limits and Structures in Graph Theory
Publication details
- Journal / source
- Designs Codes and Cryptography
- Publisher
- Springer Science and Business Media LLC
- Volume
- 94
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN