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Teaching

Throughout Rhian’s PhD studies, she took on the role of Visiting Lecturer, teaching on various modules throughout the BSc. Rhian has taught a combination of undergraduate modules, such as Finite Mathematics, Statistical Methods, Linear Programming, Quality Control, Mathematical Modelling and computational programming such as MATLAB and R. She has also taught mathematics to computer science students. Rhian is actively involved in outreach holding annual revision courses for A Level students.

Research

Rhian’s research is centred around group algebras and coding theory; her PhD thesis is entitled “Group Rings: Units and Their Applications in Self-Dual Codes”. Throughout her PhD, Rhian published four papers, with a further two in submission. In recent years, Rhian has focussed on the use of group rings in algebraic coding theory in order to construct self-dual and extremal self-dual codes.

 

Published Work

  • (with J. Gildea) Units of the group algebra of the group Cn x D6 over any finite field of characteristic 3 (International Electronic Journal of Algebra)
  • (with S. Dougherty, J. Gildea & A. Tylyshchak) Group Rings, G-Codes and Constructions of Self-Dual and Formally Self-Dual Codes (Designs, Codes & Cryptography)
  • (with S. Dougherty, J. Gildea & A. Tylyshchak) Constructions for Self-Dual and Formally Self-Dual Codes from Group Rings (Finite Fields and Their Applications)
  • (with J. Gildea, A. Kaya & A. Tylyshchak) Double Bordered Constructions of Self-Dual codes from Group Rings over Frobenius Rings (Cryptography and Communications)
  • (with J. Gildea, A. Kaya & A. Tylyshchak) New Self-Dual Codes from 2x2 Block Circulant Matrices, Group Rings and Neighbours of Neighbours (https://arxiv.org/abs/2002.09789)
  • (with J. Gildea, A. Kaya & A. Tylyshchak, B.Yildiz) New Extremal Binary Self-Dual Codes from Block Circulant Matrices and  Block Quadratic Residue Circulant Matrices (https://arxiv.org/abs/2003.05296)

Qualifications

BSc, MSc.