𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On substructures of abelian difference sets with classical parameters

✍ Scribed by Kevin Jennings

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
121 KB
Volume
16
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We constrain the structure of difference sets with classical parameters in abelian groups. These include the classical Singer 7 and Gordon et al. 4 constructions and also more recent constructions due to Helleseth et al. 5, 6 arising from the study of sequences with ideal autocorrelation properties. A unified overview of the known families is given in 3 and 3. We show here that any abelian difference set with these parameters inherits a very regular intersection property with regard to subgroups. We show in particular that a planar difference set can always be found embedded in an abelian difference set of odd order whose parameters are those of a 5‐dimensional projective geometry. Β© 2008 Wiley Periodicals, Inc. J Combin Designs 16: 182–190, 2008

πŸ“œ SIMILAR VOLUMES

Cyclic Relative Difference Sets with Cla
Cyclic Relative Difference Sets with Classical Parameters
✍ K.T. Arasu; J.F. Dillon; Ka Hin Leung; Siu Lun Ma πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 121 KB

We investigate the existence of cyclic relative difference sets with parameters ((q d &1)Γ‚(q&1), n, q d&1 , q d&2 (q&1)Γ‚n), q any prime power. One can think of these as ``liftings'' or ``extensions'' of the complements of Singer difference sets. When q is odd or d is even, we find that relative diff

Constructions of Relative Difference Set
Constructions of Relative Difference Sets with Classical Parameters and Circulant Weighing Matrices
✍ Ka Hin Leung; Siu Lun Ma; Bernhard Schmidt πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 173 KB

In this paper, a new family of relative difference sets with parameters Γ°m; n; k; lÞ ΒΌ ððq 7 Γ€ 1Þ=Γ°q Γ€ 1Þ; 4Γ°q Γ€ 1Þ; q 6 ; q 5 =4Þ is constructed where q is a 2-power. The construction is based on the technique used in [2]. By a similar method, we also construct some new circulant weighing matrices