𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Difference sets in dihedral groups

✍ Scribed by Ka Hin Leung; Siu Lun Ma; Yan Loi Wong

Publisher
Springer
Year
1991
Tongue
English
Weight
221 KB
Volume
1
Category
Article
ISSN
0925-1022

No coin nor oath required. For personal study only.

✦ Synopsis

~ study the existence of nontrivial (2m, k, X )-difference sets in dihedral groups. Some nonexistence results are proved. In particular, we show that n = k -3, is odd and Β’(n)/n < 112. Finally, a computer search shows that, except 5 undecided cases, no nontrivial difference set exists in dihedral groups for n _< 106.

πŸ“œ SIMILAR VOLUMES

Asymptotic Nonexistence of Difference Se
Asymptotic Nonexistence of Difference Sets in Dihedral Groups
✍ Ka Hin Leung; Bernhard Schmidt πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 190 KB

We prove that for any primes p 1 ; . . . ; p s there are only finitely many numbers Q s iΒΌ1 p ai i ; a i 2 Z ΓΎ ; which can be orders of dihedral difference sets. We show that, with the possible exception of n ΒΌ 540; 225; there is no difference set of order n with 15n410 6 in any dihedral group.

New partial difference sets in p-groups
New partial difference sets in p-groups
✍ Xiang-Dong Hou πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 110 KB

## Abstract Latin square type partial difference sets (PDS) are known to exist in __R__ Γ— __R__ for various abelian __p__‐groups __R__ and in β„€^__t__^. We construct a family of Latin square type PDS in β„€^__t__^ Γ— β„€^2__nt__^~__p__~ using finite commutative chain rings. When __t__ is odd, the ambient