6 papers
A Survey of the Hadamard Maximal Determinant Problem
Patrick Browne, Ronan Egan, Fintan Hegarty +1
In a celebrated paper of 1893, Hadamard established the maximal determinant theorem, which establishes an upper bound on the determinant of a matrix with complex entries of norm at…
Homomorphisms of matrix algebras and constructions of Butson-Hadamard matrices
Padraig O Cathain, Eric Swartz
An matrix is Butson-Hadamard if its entries are roots of unity and it satisfies . Write for the set of such matrices. Suppo…
Spectra of Hadamard matrices
Ronan Egan, Padraig O Cathain, Eric Swartz
A Butson Hadamard matrix has entries in the kth roots of unity, and satisfies the matrix equation . We write for the set of such matrice…
Construction of the outer automorphism of S6 via a complex Hadamard matrix
Neil Gillespie, Padraig Ó Catháin, Cheryl Praeger
We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots o…
Improved User-Private Information Retrieval via Finite Geometry
Oliver Gnilke, Marcus Greferath, Camilla Hollanti +3
In a User-Private Information Retrieval (UPIR) scheme, a set of users collaborate to retrieve files from a database without revealing to observers which participant in the scheme r…
Compressed sensing with combinatorial designs: theory and simulations
Darryn Bryant, Charles Colbourn, Daniel Horsley +1
In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use…