Divisible designs and semi-regular relative difference sets from additive Hadamard cocycles

Authors:
Yu Qing Chen
Affiliations:
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435-0001, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

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Abstract

Additive Hadamard cocycles are a natural generalization of presemifields. In this paper, we study divisible designs and semi-regular relative difference sets obtained from additive Hadamard cocycles. We show that the designs obtained from additive Hadamard cocycles are flag transitive. We introduce a new product construction of Hadamard cocycles. We also study additive Hadamard cocycles whose divisible designs admit a polarity in which all points are absolute. Our main results include generalizations of a theorem of Albert and a theorem of Hiramine from presemifields to additive Hadamard cocycles. At the end, we generalize Maiorana-McFarland@?s construction of bent functions to additive Hadamard cocycles.