Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Entire DC Network
Exponent Bounds For A Family Of Abelian Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Siu Lun Ma, Robert L. Mcfarland
Exponent Bounds For A Family Of Abelian Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Siu Lun Ma, Robert L. Mcfarland
Department of Math & Statistics Faculty Publications
Which groups G contain difference sets with the parameters (v, k, λ)= (q3 + 2q2 , q2 + q, q), where q is a power of a prime p? Constructions of K. Takeuchi, R.L. McFarland, and J.F. Dillon together yield difference sets with these parameters if G contains an elementary abelian group of order q2 in its center. A result of R.J. Turyn implies that if G is abelian and p is self-conjugate modulo the exponent of G, then a necessary condition for existence is that the exponent …
A Survey Of Hadamard Difference Sets, James A. Davis, Jonathan Jedwab
A Survey Of Hadamard Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1, d2 ∈ D, d1 ≠ d2} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic according to the properties of the underlying group. Difference sets are important in design theory because they are equivalent to symmetric (v, k, λ) designs with a regular automorphism group [L].
A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
Department of Math & Statistics Faculty Publications
We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets.