dc.contributor.advisor Gildea, Joe en dc.contributor.author O'Neill, Harrison T. * dc.date.accessioned 2018-03-26T14:45:58Z dc.date.available 2018-03-26T14:45:58Z dc.date.issued 2017-10-09 dc.identifier.citation O'Neill, H. T. (2017). Group Algebras and Their Applications. (Masters thesis). University of Chester, United Kingdom. en dc.identifier.uri http://hdl.handle.net/10034/621032 dc.description.abstract Let 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. dc.language.iso en en dc.publisher University of Chester en dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ * dc.subject mathematics en dc.subject Coding Theory en dc.subject Group rings en dc.title Group Algebras and Their Applications en dc.type Thesis or dissertation en dc.type.qualificationname MSc en dc.type.qualificationlevel Masters Degree en refterms.dateFOA 2018-08-13T14:15:57Z html.description.abstract Let 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.
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