Existence Status of Some Previously Open Abelian Difference Sets
Document Type
Article
Publication Date
7-28-2006
Abstract
The paper establishes the existence status of several previously open abelian difference sets. In particular, the authors prove the nonexistence of all but finitely many McFarland difference sets with parameters (qd+1(s+1),qd(qd+1−1q−1),qd(qd−1q−1))(q^{d+1}(s+1), q^d(\frac{q^{d+1}-1}{q-1}), q^d(\frac{q^d-1}{q-1}))(qd+1(s+1),qd(q−1qd+1−1),qd(q−1qd−1)) where s=qd+1−1q−1s=\frac{q^{d+1}-1}{q-1}s=q−1qd+1−1. They also determine the existence or nonexistence of several specific Hadamard and Menon difference sets using character theory, algebraic number theory, and computational methods.
Repository Citation
Arasu, K. T.,
Burkett, G.,
& Linger, M.
(2006). Existence Status of Some Previously Open Abelian Difference Sets. Discrete Mathematics, 306 (14), 1467-1473.
https://corescholar.libraries.wright.edu/math/556
DOI
10.1016/j.disc.2005.06.031
