Group-like algebras and Hadamard matrices

Group 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....

Nonexistence Results for Hadamard-like Matrices

The class of square (0, 1,−1)-matrices whose rows are nonzero and mutually orthogonal is studied. This class generalizes the classes of Hadamard and Weighing matrices. We prove that if there exists an n by n (0, 1,−1)-matrix whose rows are nonzero, mutually orthogonal and whose first row has no zeros, then n is not of the form pk, 2pk or 3p where p is an odd prime, and k is a positive integer.

Cryptographic Boolean functions via group Hadamard matrices

For any integers n m n m n we construct a set of boolean functions on Vm say ff z fn z g which has the following important cryptographic properties i any nonzero linear combination of the functions is balanced ii the nonlinearity of any nonzero linear combination of the functions is at least m n iii any nonzero linear combination of the functions satis es the strict avalanche cri terion iv the ...

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

Hadamard and Conference Matrices

We discuss new constructions of Hadamard and conference matrices using relative difference sets. We present the first example of a relative (n, 2, n − 1, n−2 2 )-difference set where n − 1 is not a prime power.