Publications

Improved user-private information retrieval via finite geometry. The 10th International Workshop on Coding and Cryptography (2017). Joint work with Padraig Ó Catháin, Eric Swartz, Oliver Gnilke, Camilla Hollanti and Marcus Greferath. We generalize work of Swanson and Stinson to construct communication protocols in which users retain privacy even after the defection of a coalition of users whose size grows as a root function of the total number of users. Previous protocols could be compromised by a finite number of users.

Improved user-private information retrieval via finite geometry. Designs, Codes and Cryptography, 87 (2-3), 665-677 (2019).
Joint work with Padraig Ó Catháin, Eric Swartz, Oliver Gnilke, Camilla Hollanti and Marcus Greferath. Journal version of publication 1 on this list. We extended that paper to include analysis of the known families of generalised quadrangles. 

Morphisms of Skew Hadamard Matrices. Bull. Inst. Combin. Appl. 90 (2020), 50-62.
Joint work with Padraig Ó Catháin, Philip Heikoop and Jack Pugmire. We consider morphisms from Quaternary Unit Hadamard matrices (introduced by Fender, Kharaghani and Suda) to real Hadamard matrices. The construction recovers a classic result of Mukhopadhyay and Seberry. We also find nonexistence conditions for QUH matrices by considering the splitting of prime ideals in biquadratic number fields.

Invariants of quadratic forms and applications in design theory. Linear Algebra Appl. 682, 1–27, (2024).
Joint work with Oliver Gnilke, Oktay Olmez, and Padraig Ó Catháin.