4 citations · 5 across the 6 of their papers we have counts for
6 papers · 1 filter
Invariants of Quadratic Forms and applications in Design Theory
Oliver W. Gnilke, Padraig O Cathain, Oktay Olmez +1
The study of regular incidence structures such as projective planes and symmetric block designs is a well established topic in discrete mathematics. Work of Bruck, Ryser and Chowla…
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…
Remark on a result of Constantine
Padraig Ó Catháin
In this short note we construct codes of length with codewords and minimum distance whenever is the order of a Hadamard matrix. This generalises work of C…