Publications

My publications and preprints to date are for the most part in fields related to Discrete Mathematics - typically Design Theory and Coding Theory. Aspects of several different branches of pure mathematics such as Group Theory, Linear Algebra, and Number Theory feature prominently. Published papers are listed in order of their first online appearance (rather than by the appearance of print versions, which is why the years are sometimes out of order) with links to the articles provided. A preprint version is also linked, but there may be some discrepancies between this and the published version. A list of titles of submitted preprints follows, but usually with no link prior to publication (although a version may be posted on arXiv). Unsubmitted preprints and works in progress are not listed. The journals for which I have acted as an academic referee are also listed below.

Publications

1. D. L. Flannery, R. Egan, On linear shift representations, J. Pure Appl. Algebra, 219, 8, 3482-3494, 2015. (Preprint)

2. R. Egan, D. L. Flannery, P. Ó Catháin, Classifying cocyclic Butson Hadamard Matrices, Algebraic Design Theory and Hadamard Matrices, Springer Proc. Math. Stat., 133, 93-106, 2015. (Preprint)

3. R. Egan, D. L. Flannery, Automorphisms of generalized Sylvester matrices, Discrete Math., 340, 3, 516-523, 2017. (Preprint)

4. R. Egan, On equivalence of negaperiodic Golay pairs, Des. Codes Cryptogr., 85, 3, 523-532, 2017. (Preprint)

5. D. Crnković, R. Egan, A. Švob, Orbit matrices of Hadamard matrices and related codes, Discrete Math., 341, 5, 1199-1209, 2018. (Preprint)

6. D. Crnković, R. Egan, A note on Siamese twin designs intersecting in a BIBD and a PBD, Math. Comput. Sci., Vol 12, 4, 389-395, 2018. (Preprint)

7. R. Egan, Phased unitary Golay pairs, Butson Hadamard matrices and a conjecture of Ito's, Des. Codes Cryptogr., 87, 1, 67-74, 2019. (Preprint)

8. D. Crnković, R. Egan, A. Švob, Constructing self-orthogonal and Hermitian self-orthogonal codes via weighing matrices and orbit matrices, Finite Fields Appl., 55, 64-77, 2019. (Preprint)

9. R. Egan, P. Ó Catháin, E. Swartz, Spectra of Hadamard matrices, Australas. J. Combin., 73(3), 501-512, 2019. (Preprint)

10. R. Egan, P. Ó Catháin, Morphisms of Butson Classes, Linear Algebra Appl., 577, 78-93, 2019. (Preprint)

11. D. Crnković, R. Egan, A. Švob, Self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs, Adv. Math. Commun., 14, 4, 591-602, 2020. (Preprint)

12. D. Crnković, R. Egan, B. Rodrigues, A. Švob, LCD codes from weighing matrices, Appl. Algebra Engrg. Comm. Comput., 32, 175-189, 2021. (Preprint)

13. R. Egan, Generalizing pairs of complementary sequences and a construction of combinatorial structures, Discrete Math., 343, 5, 111795, 2020. (Preprint)

14. J. A. Armario, I Bailera, R. Egan, Generalized Hadamard full propelinear codes, Des. Codes Cryptogr., 89, 599-615, 2021. (Preprint)

15. D. Crnković, D. Dumičić Danilović, R. Egan, A. Švob, Periodic Golay pairs and pairwise balanced designs, J. Algebr Comb., 55, 245-257, 2022. (Preprint)

16. P. Browne, R. Egan, F. Hegarty, P. Ó Catháin, A survey of the Hadamard maximal determinant problem, Electron. J. Combin., 28, 4, P4.41, 2021. (arXiv preprint)

17. J. A. Armario, I Bailera, R. Egan, Butson full propelinear codes, Des. Codes. Cryptogr., 91, 333-351, 2023. (arXiv preprint)

18. J. A. Armario, R. Egan, D. L. Flannery, Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices, Cryptogr. Commun., 16, 323-337, 2024. (arXiv preprint)

Preprints

R. Egan, A survey of complex generalized weighing matrices and a construction of quantum error-correcting codes. (arXiv preprint) 

M. Shi, D. Lu, J. A. Armario, R. Egan, F. Ozbudak, P. Solé, Butson Hadamard matrices, bent sequences, and spherical codes. (arXiv preprint)

PhD Thesis

My PhD thesis - "Topics in cocyclic development of pairwise combinatorial designs" - is not published, although most of the novel material appears in some form in the publications [1-4] above. However it is available online and open access in the University of Galway repository, here.

Peer-Reviewing

To date I have refereed articles for the following journals: Discrete Mathematics; Designs Codes and Cryptography; Journal of Combinatorial Designs; Electronic Journal of Combinatorics; IEEE Transactions on Information Theory; Australasian Journal of Combinatorics; Journal of Symbolic Computing; Cryptography and Communications; Communications in Mathematics, Mathematics in Computer Science; Journal of Algebraic Combinatorics; Applicable Algebra in Engineering Communication and Computing; Bulletin of the ICA; Publicacions Matemàtiques.