Difference sets and doubly transitive actions on Hadamard matrices
نویسندگان
چکیده
منابع مشابه
Difference sets and doubly transitive actions on Hadamard matrices
Non-affine groups acting doubly transitively on a Hadamard matrix have been classified by Ito. Implicit in this work is a list of Hadamard matrices with non-affine doubly transitive automorphism group. We give this list explicitly, in the process settling an old research problem of Ito and Leon. We then use our classification to show that the only cocyclic Hadamard matrices developed form a dif...
متن کاملGroup actions on Hadamard matrices
Faculty of Arts Mathematics Department Master of Literature by Padraig Ó Catháin Hadamard matrices are an important item of study in combinatorial design theory. In this thesis, we explore the theory of cocyclic development of Hadamard matrices in terms of regular group actions on the expanded design. To this end a general theory of both group development and cocyclic development is formulated....
متن کاملNote on Hadamard groups and difference sets
A representation theoretical characterization of an Hadamard subset is given. §l. Introduction. A finite group G of order 2n is called an Hadamard group if G contains an n-subset D and an element e* such that (1) D and De*,are disjoint, (2) D and Da intersect exactly in n/2 elements for any element a of G distinct from e* and the identity element e of G, and (3) Da and {b, be*} intersect exactl...
متن کاملOn Generalized Hadamard Matrices and Difference Matrices: Z6
(Caution: please note Jennifer Seberry has tried but been unable to contact the persons named as co-authors. Apolgogies for half finished results.) We note that the literature on this subject is very disorganized. Authors have not read the literature on their own key-words and papers thus ignored, on the other hand papers have been claimed to be published which have not. We have put together th...
متن کاملThe 2-transitive complex Hadamard matrices
We determine all possibilities for a complex Hadamard matrix H admitting an automorphism group which permutes 2-transitively the rows of H. Our proof of this result relies on the classification theorem for finite 2-transitive permutation groups, and thereby also on the classification of finite simple groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2012
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2012.02.011