Dr Santiago Barrera Acevedo

Research Overview

My research interest lies in the interplay between algebra and combinatorics, particularly, in the emerging area of algebraic design theory. This is the area of mathematics concerned with the application of algebra and algebraic modes of reasoning to solve problems in combinatorics, specifically, questions arising from design theory. My current research focuses on the construction and classification of cocylic Hadamard matrices and other orthogonal designs; techniques of group cohomology and representation theory of finite groups are used for such purposes.

Selected Publications

[1] Barrera Acevedo, Santiago ; Cathain, Padraig O. ; Dietrich, Heiko. "Constructing cocyclic Hadamard matrices of order 4p". In: Journal of Combinatorial Designs. 2019 ; Vol. 27, No. 11. pp. 627-642. https://doi.org/10.1002/jcd.21664

[2] Barrera Acevedo, Santiago ; Dietrich, Heiko. "New infinite families of Williamson Hadamard matrices". In: Australasian Journal of Combinatorics. 2019 ; Vol. 73, No. 1. pp. 207-219.

[3] Barrera Acevedo, Santiago ; Dietrich, Heiko. "Perfect sequences over the quaternions and (4n, 2, 4n, 2n)-relative difference sets in Cn × Q 8". In: Cryptography and Communications: discrete structures, Boolean functions and sequences. 2018 ; Vol. 10, No. 2. pp. 357-368. https://doi.org/10.1007/s12095-017-0224-y

[4] Barrera Acevedo, Santiago ; Dietrich, Heiko. "Relative Difference Sets and Hadamard Matrices from Perfect Quaternionic Arrays". In: Mathematics in Computer Science. 2018 ; Vol. 12, No. 4. pp. 397–406. https://doi.org/10.1007/s11786-018-0376-y

[5] Barrera Acevedo, Santiago ; Jolly, Nathan James. "Perfect arrays of unbounded sizes over the basic quaternions". In: Cryptography and Communications: discrete structures, Boolean functions and sequences. 2014 ; Vol. 6, No. 1. pp. 47 - 57. https://doi.org/10.1007/s12095-013-0086-x