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On substructures of abelian difference sets with classical parameters
Author(s) -
Jennings Kevin
Publication year - 2008
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20172
Subject(s) - mathematics , difference set , abelian group , ideal (ethics) , combinatorics , intersection (aeronautics) , set (abstract data type) , order (exchange) , planar , pure mathematics , discrete mathematics , philosophy , computer graphics (images) , epistemology , finance , computer science , engineering , economics , programming language , aerospace engineering
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. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 182–190, 2008
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