scholarly journals On the Existence of (v,k,λ) Difference Sets with k<1250 and k−λ Is a Square

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Adegoke Solomon Osifodunrin
Keyword(s):  
Difference Sets ◽  
Variance Technique ◽  
Sylow Theorem

We combine Turyn's self-conjugacy result, variance technique, Dillon dihedral trick, and Sylow theorem to investigate the existence of (v,k,λ) difference sets in which k−λ is a square and k<1250.

A SIMPLE WAY TO ESTABLISH NON-EXISTENCE OF DIFFERENCE SETS

2012 ◽  
Vol 04 (01) ◽  
pp. 1250007
Author(s):  
ADEGOKE S. OSIFODUNRIN
Keyword(s):  
Difference Sets ◽  
Variance Technique

We illustrate that the combination of the variance technique and factorization in the cyclotomic rings is sufficient to establish non-existence of difference sets.

scholarly journals Graphs of vectorial plateaued functions as difference sets

2021 ◽  
Vol 71 ◽  
pp. 101795
Author(s):  
Ayça Çeşmelioğlu ◽  
Oktay Olmez
Keyword(s):  
Difference Sets ◽  
Plateaued Functions

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).

scholarly journals Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets

1999 ◽  
Vol 87 (1) ◽  
pp. 74-119 ◽  
Author(s):  
Ronald Evans ◽  
Henk D.L. Hollmann ◽  
Christian Krattenthaler ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Gauss Sums ◽  
Cyclic Difference Sets ◽  
Jacobi Sums

scholarly journals Difference sets and computability theory

1998 ◽  
Vol 93 (1-3) ◽  
pp. 63-72
Author(s):  
Rod Downey ◽  
Zoltán Füredi ◽  
Carl G. Jockusch ◽  
Lee A. Rubel
Keyword(s):  
Difference Sets ◽  
Computability Theory
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