Department: Mathematics and Statistics
Academic Qualifications
2018: PhD in Mathematics, University of the Western Cape, South Africa. (Thesis title:
Codes, graphs and designs from maximal subgroups of alternating groups.)
2012–2013: MSc Mathematical Sciences, African Institute for Mathematical Sciences (AIMS),
South Africa. (Thesis title: Codes and graphs from alternating groups An for n odd.)
2007–2009: MSc Information Theory, Coding and Cryptography with Distinction, Mzuzu
University, Malawi. (Thesis title: The weight distribution of inequivalent Goppa codes.)
2002–2006: BEd(Science) with strong credit, University of Malawi, Chancellor College.
Academic short courses2018: Winter School: Axial Algebras, Modern Permutation Groups and Applications to Coding Theory, Durban , South Africa.
2015: Winter School: Algebraic Representation Theory and Applications, African Institute
for Mathematical Sciences(AIMS), Cape Town, South Africa.
2009: Advanced School on Knot Theory and its applications to Physics and Biology, International Center for Theoretical Physics (ICTP), Trieste, Italy.
Publications
N. B. Mumba, W. Fish, E. Mwambene and B. G. Rodrigues, Binary codes and partial
permutation decoding sets from biadjacency matrices of bipartite graphs Γ(2k, k, k+1, 1),
Quest. Math., (2019), 1–16.
N. B. Mumba and E. Mwambene, Automorphism groups of graph covers and uniform
subset graphs, AKCE Int. J. Graphs Comb., 15, (2018), 27–33.
N. B. Mumba, W. Fish, E. Mwambene and B. G. Rodrigues, Binary codes and partial
permutation decoding sets from biadjacency matrices of bipartite graphs Γ(2k + 1, k, k +
2, 1), Graphs Combin., 33, (2017), 357–368.
N. B. Mumba, W. Fish and E. Mwambene, Equality of codes in the face of nonisomorphism in uniform subset graphs, revised.
N. B. Mumba, Diameter and automorphism groups of bipartite graphs (n, k, l, 1),
revised.
International journal publications
N. B. Mumba, W. Fish and E. Mwambene, Codes from generalised uniform subset
graphs Γ(2k, k, i) for i ∈ {1, k − 1} submitted.
N. B. Mumba, Binary codes from biadjacency matrices of bipartite graphs Γ(2k +
r, k, k + 1 + r, 1) submitted.
Preprints, An efficient way for solving a special case of a non-homogeneous linear second order
differential equation, preprint, 2013.
Knots and graphs, preprint, 2013.
A formula for solving a special case of Cauchy-Euler Ordinary Differential Equations,
preprint, 2019.
International conference presentations
2016: “Binary codes and partial permutation decoding sets from biadjacency matrices of bipartite graphs Γ(2k, k, k + 1, 1),” Proc. SAMS’16, Cape Town, South Africa.
2013: “ Codes, graphs and designs from Alternating groups An for n odd, ”Proc. SAMSA’13,
Cape Town, South Africa.
2010: “An efficient way of finding a particular solution of a differential equation,”Proc. SAMSA’10,
Gaborone, Botswana.
2009: “Another approach to Goppa codes,”Proc. IEEE AFRICON 2009.
2009: “The uniqueness of Hamming codes,”Proc. SAMSA’09, Dar Es Salaam, Tanzania.
2008: “The weight distribution of inequivalent Goppa codes”Proc. SAMSA’08, Maputo,
Mozambique.
Theses and other publications
2017: PhD thesis, Mumba N.B, Mwambene E, Fish W, Rodrigues B, Codes, graphs and designs
from maximal subgroups of alternating groups, http://etd.uwc.ac.za/handle/11394/6165.
2013: MSc. thesis, Mumba N.B, Mwambene E, Rodrigues B, Codes and graphs from Alternating groups An for n odd,
http://archive.aims.ac.za/structured-masters-research-projects/2012-13.
2009: MSc. thesis, Mumba N.B, Ryan J.A, The weight distribution of inequivalent Goppa
codes, Mzuzu university.
Research Interests
Coding Theory,
Graph Theory,
Combinatorics,
Group Theory.
Postgraduate research supervision
Supervised three MSc. students in the areas of coding and graph theory in 2018–2019
academic year.
Professional affiliations
2018–Present: Mhub Mathematics/Statistics Consultant.
2013–2017: South African Mathematics Society (SAMS)–Member
2010–Present: Institute of Chartered Accountants in Malawi (ICAM)–Examiner/marker in
Business Mathematics and Statistics.
2008–Present: Southern Africa Mathematical Sciences Association(SAMSA)–Member.