Gildea, JoeO'Neill, Harrison T.2018-03-262018-03-262017-10-09O'Neill, H. T. (2017). Group Algebras and Their Applications. (Masters thesis). University of Chester, United Kingdom.http://hdl.handle.net/10034/621032Let RG be the group ring of the group G and the ring R. If R is a field, we usually refer to RG as a group algebra. We initially describe the unit group of the group algebra F2 kD8 where F2 k is a Galois Field of 2k elements and D8 is the dihedral group of order 8. We then describe the unitary unit group of F2 kD8. Furthermore, we show the connection between unitary units in group rings and self-dual codes. Finally, we construct certain self-dual codes from the unitary units of the group algebra F2 kD8.enhttp://creativecommons.org/licenses/by-nc-nd/4.0/mathematicsCoding TheoryGroup ringsThesis or dissertation