I am interested in finite group theory and its interplay with various combinatorial structures, including designs, codes, graphs, and impartial games. Currently, I am working on the construction of designs and codes that are invariant under finite primitive groups, with a particular focus on applying modular representation theory to construct linear codes invariant under these groups.
My research establishes connections between coding theory, game theory, cryptography, and combinatorial design theory, and often involves collaboration across algebra and combinatorics.
Below is a selected list of my recent publications.
Selected list of Publications
With H Saydi, Impartial Generation and Avoidance Games Restricted to a Conjugacy Class of finite Groups, submitted.
On point and block primitive designs invariant under permutation groups, submitted. https://arxiv.org/abs/2409.09730
With H Saydi, Some designs from the conjugacy classes of linear groups, to appear in J. Algebra Appl.
With BG Rodrigues, On some minimal linear codes invariant under the Chevalley group F4(2), to appear in Cryptography and Communications.
With Nyikadzino TG and TT Seretlo, Structure of linear codes invariant under the unitary group U(3,3), to appear in Algebraic Structures and Their Applications, 2025. https://doi.org/10.22034/as.2026.22222.1744
With H. Saydi and T. Seretlo, A new method for constructing designs and codes from conjugacy classes, Des. Codes Cryptogr., 94, 11 (2026). https://doi.org/10.1007/s10623-025-01774-x
With M.J. Kekana and T. Seretlo, Some designs from fixed points of alternating groups, Trans. Comb., 15 (1), 47-54, 2026. https://doi.org/10.22108/toc.2025.141435.2178
With C.K. Mokalapa and T. Seretlo, On designs from the character tables of finite groups, Khayyam J. Math., 11 (2025), no. 2, 74–387. https://doi.org/10.22034/kjm.2025.511987.3483
With MR Darafsheh and BG Rodrigues, On linear codes constructed from finite groups with a trivial Schur multiplier, Mathematical Communications, 28 (2023), 85–104. https://hrcak.srce.hr/file/437411
Finite groups whose commuting conjugacy class graphs have isolated vertices, Communications in Algebra, 51(2), 2023, 648–656. https://doi.org/10.1080/00927872.2022.2107213
Reduced designs constructed by Key-Moori Method 2 and their connection with Method 3, AUT Journal of Mathematics and Computing, 4(1), 2023, 39–46.
Designs and codes from fixed points of alternating groups, Communications in Algebra, 50(5), 2022, 2215–2222. https://doi.org/10.22060/ajmc.2022.21378.1092
With J. Moori, B. Rodrigues, and S. Zandi, Designs from maximal subgroups and conjugacy classes of Ree groups, Advances in Mathematics of Communications, 14(4), 2020, 603–611. https://doi.org/10.3934/amc.2020033
With J. Moori, B. Rodrigues, and S. Zandi, Some symmetric designs invariant under the small Ree groups, Communications in Algebra, 47(5), 2019, 2131–2148. https://doi.org/10.1080/00927872.2018.1530245
With J. Moori, Some designs invariant under Suzuki groups, Utilitas Mathematica, 109, 2018, 105–114. https://www.researchgate.net/PDF
With J. Moori, Constructing some designs invariant under PSL2(q), q even, Communications in Algebra, 46(1), 2018, 160–166. https://doi.org/10.1080/00927872.2017.1316854
With J. Moori, Some designs and codes invariant under the Tits group, Advances in Mathematics of Communications, 11(1), 2017, 77–82. https://doi.org/10.3934/amc.2017003
Finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels, Quaestiones Mathematicae, 39(4), 2016, 523–530. https://doi.org/10.2989/16073606.2015.1096858
Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character, Open Math. (formerly Cent. Eur. J. Math.), 12(1), 2014, 79–83. https://link.springer.com/article/10.2478/s11533-013-0327-4
On the number of the irreducible characters of factor groups, Int. J. Group Theory, 2(2), 2013, 19–23.
With S. Zandi, The number of conjugacy classes contained in normal subgroups of solvable groups, J. Algebra Appl., 12, 1250204, 2013, 10 pages. https://doi.org/10.1142/S0219498812502040
With H. Doostie, Finite ppp-groups with few nonlinear irreducible character kernels, Bull. Iran. Math. Soc., 38(2), 2012, 413–422. https://bims.iranjournals.ir/article.pdf
With H. Doostie, On the degrees of the nonlinear irreducible characters in finite groups, Extr. Math., 26(1), 2011, 145–151. https://matematicas.unex.es/~extracta/Vol-26-1/26B1Doos.pdf
With A. Iranmanesh, Finite groups with a unique nonlinear nonfaithful irreducible character, Arch. Math. (Brno), 47, 2011, 91–99. https://am-brno.math.muni.cz/11-2/am1729.pdf