6 papers · 1 filter
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…
Generalized Hadamard full propelinear codes
José Andrés Armario, Ivan Bailera, Ronan Egan
Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new cl…
LCD codes from weighing matrices
Dean Crnkovic, Ronan Egan, B. G. Rodrigues +1
Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD cod…
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…
Morphisms of Butson classes
Ronan Egan, Padraig Ó Catháin
We introduce the concept of a morphism from the set of Butson Hadamard matrices over kth roots of unity to the set of Butson matrices over th roots of unity. As concrete exam…
Classifying cocyclic Butson Hadamard matrices
Ronan Egan, Dane Flannery, Padraig Ó Catháin
We classify all the cocyclic Butson Hadamard matrices of order over the th roots of unity for an odd prime and . That is, we compile a lis…