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 and TT Seretlo, A new method for constructing designs and codes from the conjugacy classes of groups, to appear in Designs, Codes and Cryptography, 2026.
With MJ Kekana and TT Seretlo, Some designs from the fixed points of alternating groups, to appear in Transactions on Combinatorics, 2026.
With CK Mokalapa and TT Seretlo, on designs from the character tables of finite groups, to appear in Khayyam Journal of Mathematics, 2025.
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.
On point and block primitive designs invariant under permutation groups, submitted.
With H Saydi, Some designs from the conjugacy classes of linear groups, submitted.
With BG Rodrigues, On some minimal linear codes invariant under the Chevalley group F4(2), submitted.
With MR Darafsheh and BG Rodrigues, On linear codes constructed from finite groups with a trivial Schur multiplier, Mathematical Communications, 28 (2023), 85–104.
Finite groups whose commuting conjugacy class graphs have isolated vertices, Communications in Algebra, 51(2), 2023, 648–656.
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.
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.
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.
With J. Moori, Some designs invariant under Suzuki groups, Utilitas Mathematica, 109, 2018, 105–114.
With J. Moori, Constructing some designs invariant under PSL2(q), q even, Communications in Algebra, 46(1), 2018, 160–166.
With J. Moori, Some designs and codes invariant under the Tits group, Advances in Mathematics of Communications, 11(1), 2017, 77–82.
Finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels, Quaestiones Mathematicae, 39(4), 2016, 523–530.
Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character, Open Math. (formerly Cent. Eur. J. Math.), 12(1), 2014, 79–83.
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.
With H. Doostie, Finite ppp-groups with few nonlinear irreducible character kernels, Bull. Iran. Math. Soc., 38(2), 2012, 413–422.
With H. Doostie, On the degrees of the nonlinear irreducible characters in finite groups, Extr. Math., 26(1), 2011, 145–151.
With A. Iranmanesh, Finite groups with a unique nonlinear nonfaithful irreducible character, Arch. Math. (Brno), 47, 2011, 91–99.