Mathematical Sciences Department, Discrete Math Seminar - Guillermo Nunez Ponasso, WPI "The asymptotic existence of Butson-type Hadamard matrices" (UH405)
3:00 pm to 3:50 pm
Mathematical Sciences Department
Discrete Math Seminar
Speaker: Guillermo Nunez Ponasso, Post-Doctoral Scholar, Department of Electrical Engineering, WPI
Monday, October 9, 2023
3:00 - 3:50 pm
Unity Hall 405
Title: The asymptotic existence of Butson-type Hadamard matrices
Abstract: A Butson-type Hadamard matrix is a square matrix with roots of unity entries and whose rows are orthogonal. Their names comes from a well-known result due to Butson, which shows that for every prime number p there exist Butson-type matrices of order 2p over the p-th roots of unity. This result was further extended by Dawson, who showed that there are always Butson-type matrices of order 4p over the p-th roots. Later, Dawson and de Launey showed that this also holds orders hp where h is the order of a real Hadamard matrix, and p is a large enough prime.
In this talk, I will present the results of Dawson and de Launey, together with my own contribution sharpening the known lower bounds for the existence of Butson-type matrices of order 12p.