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A Unified Approach To Difference Sets With Gcd(V, N) > 1, James A. Davis, Jonathan Jedwab
A Unified Approach To Difference Sets With Gcd(V, N) > 1, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
The five known families of difference sets whose parameters (v, k, λ; n) satisfy the condition gcd(v,n) > 1 are the McFarland, Spence, Davis-Jedwab, Hadamard and Chen families. We survey recent work which uses recursive techniques to unify these difference set families, placing particular emphasis on examples. This unified approach has also proved useful for studying semi-regular relative difference sets and for constructing new symmetric designs.
A Unifying Construction For Difference Sets, James A. Davis, Jonathan Jedwab
A Unifying Construction For Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets. The construction yields a new family of difference sets with parameters (v, k, λ,n)=(22d+4(22d+2−1)/3, 22d+1(22d+3+1)/3, 22d+1(22d+1+1)/3, 24d+2) for d⩾0. The construction establishes that a McFarland difference set exists in an abelian group of order 22 …
A Construction Of Difference Sets In High Exponent 2-Groups Using Representation Theory, James A. Davis, Ken Smith
A Construction Of Difference Sets In High Exponent 2-Groups Using Representation Theory, James A. Davis, Ken Smith
Department of Math & Statistics Faculty Publications
Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Menon difference sets (or Hadamard), and they have parameters (22d+2, 22d+1 ±2d, 22d±2d). In the abelian case, the group has a difference set if and only if the exponent of the group is less than or equal to 2d+2. In [14], the authors construct a difference set in a nonabelian group of order 64 and exponent 32. This paper generalizes that result to …