Constructions of partial difference sets and relative difference sets using Galois rings

1996 ◽  
Vol 8 (1-2) ◽  
pp. 215-227 ◽  
Author(s):  
D. K. Ray-Chaudhuri ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Relative Difference ◽  
Galois Rings ◽  
Partial Difference ◽  
Partial Difference Sets ◽  
Relative Difference Sets

scholarly journals New Partial Difference Sets in Ztp2 and a Related Problem about Galois Rings

2001 ◽  
Vol 7 (1) ◽  
pp. 165-188 ◽  
Author(s):  
Xiang-Dong Hou ◽  
Ka Hin Leung ◽  
Qing Xiang
Keyword(s):  
Related Problem ◽  
Difference Sets ◽  
Galois Rings ◽  
Partial Difference ◽  
Partial Difference Sets

scholarly journals On non-symmetric relative difference sets

2008 ◽  
Vol 37 (3) ◽  
pp. 427-435 ◽  
Author(s):  
Yutaka HIRAMINE
Keyword(s):  
Difference Sets ◽  
Relative Difference ◽  
Relative Difference Sets

Divisible Semiplanes, Arcs, and Relative Difference Sets

1987 ◽  
Vol 39 (4) ◽  
pp. 1001-1024 ◽  
Author(s):  
Dieter Jungnickel
Keyword(s):  
Projective Plane ◽  
Difference Sets ◽  
Difference Set ◽  
Relative Difference ◽  
List Type ◽  
Relative Difference Set ◽  
Large Collection ◽  
Baer Subplane ◽  
Relative Difference Sets ◽  
Definition Of

In this paper we shall be concerned with arcs of divisible semiplanes. With one exception, all known divisible semiplanes D (also called “elliptic” semiplanes) arise by omitting the empty set or a Baer subset from a projective plane Π, i.e., D = Π\S, where S is one of the following:(i) S is the empty set.(ii) S consists of a line L with all its points and a point p with all the lines through it.(iii) S is a Baer subplane of Π.We will introduce a definition of “arc” in divisible semiplanes; in the examples just mentioned, arcs of D will be arcs of Π that interact in a prescribed manner with the Baer subset S omitted. The precise definition (to be given in Section 2) is chosen in such a way that divisible semiplanes admitting an abelian Singer group (i.e., a group acting regularly on both points and lines) and then a relative difference set D will always contain a large collection of arcs related to D (to be precise, —D and all its translates will be arcs).

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