P. '. Cath'ain

activity

20152019

collaborators

4 papers

math.CO2019

Morphisms of Skew Hadamard Matrices

Philip Heikoop, Guillermo Nuñez Ponasso, Padraig Ó Catháin +1

Quaternary unit Hadamard (QUH) matrices were introduced by Fender, Kharagani and Suda along with a method to construct them at prime power orders. We present a novel construction o…

math.CO2019

Dimensions of semi-simple matrix algebras

Phillip Heikoop, Padraig Ó Catháin

For $n \geq 225$ we show that every integer of the form $n + 2 m$ such that $0 \leq 2 m \leq n^{2} - \frac{9}{2} n n$ is the dimension of a connected semi-simple subalgebra of…

math.CO2017

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 $ℓ$ th roots of unity. As concrete exam…

math.CO2015

Classifying cocyclic Butson Hadamard matrices

Ronan Egan, Dane Flannery, Padraig Ó Catháin

We classify all the cocyclic Butson Hadamard matrices $BH (n, p)$ of order $n$ over the $p$ th roots of unity for an odd prime $p$ and $n p \leq 100$ . That is, we compile a lis…