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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Chen, Yu Qing

关键词: Divisible design;    Generalized Hadamard matrix;    Bent function;    Presemifield;    Hadamard cocycle;    Relative difference set;   

DOI  :  10.1016/j.jcta.2011.04.016

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free