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Full-Text Articles in Discrete Mathematics and Combinatorics
New Semiregular Divisible Difference Sets, James A. Davis
New Semiregular Divisible Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
We modify and generalize the construction by McFarland (1973) in two different ways to construct new semiregular divisible difference sets (DDSs) with λ1≠0. The parameters of the DDS fall into a family of parameters found in Jungnickel (1982), where his construction is for divisible designs. The final section uses the idea of a K-matrix to find DDSs with a nonelementary abelian forbidden subgroup.
Hadamard Difference Sets In Nonabelian 2-Groups With High Exponent, James A. Davis, Joel E. Iiams
Hadamard Difference Sets In Nonabelian 2-Groups With High Exponent, James A. Davis, Joel E. Iiams
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 Hadamard difference sets. In the abelian case, a group of order 22t + 2 has a difference set if and only if the exponent of the group is less than or equal to 2t + 2. In a previous work (R. A. Liebler and K. W. Smith, in “Coding Theory, Design Theory, Group Theory: Proc. of the Marshall Hall Conf.,” Wiley, New York, 1992), the authors constructed a difference set in a nonabelian group of order …