Seminar: Santiago Acevedo

Perfect sequences and arrays over the quaternions, relative difference sets and Williamson Hadamard matrices

SPEAKER: Santiago Acevedo
Monash University
Date: Friday 10th August
Time: 3:00pm–4:00pm (Talk & Q/A)
Venue: Building 8 Level 9 Room 66 (AGR)
RMIT City campus

The seminar will be followed by snacks and drinks
All students, staff and visitors are welcome

ABSTRACT: The periodic autocorrelation of an array is a measure for how much the array differs from its cyclic shifts. If the autocorrelation values for all nontrivial cyclic shifts are 0, then the array is perfect. A one-dimensional array is called a sequence. It is well known that sequences with good autocorrelation properties, such as being perfect, have important applications in information technology. However, it is very difficult to construct perfect sequences over 2nd, 4th, and in general  over nth roots of unity. It is conjectured that perfect sequences over nth roots of unity do not exist for lengths greater that n2.

Due to the importance of perfect sequences and the difficulty to construct them over nth roots of unity, there has been some focus on other classes of sequences with good autocorrelation. One of these classes is the family of perfect sequences over the quaternions. In this talk I will introduce perfect sequences and arrays over the quaternion groups Q8 and Q24, and discuss their connections with relative difference sets and Williamson Hadamard matrices.

BIOGRAPHY: Santiago graduated from his PhD at Monash University in 2013, and is currently an assistant lecturer in the school of Mathematical sciences at Monash.