Cyclic And Dihedral Group Ring Codes
| dc.contributor.author | Tan, Zi Shyuan | |
| dc.date.accessioned | 2017-01-11T06:56:00Z | |
| dc.date.available | 2017-01-11T06:56:00Z | |
| dc.date.issued | 2016-08 | |
| dc.description.abstract | By generalizing the idea of viewing cyclic codes as ideals in cyclic group rings, many studies on group ring codes which are ideals, have been done since half a century ago. In 2007, T. Hurley and P. Hurley introduced a new encoding approach of codes using group rings. Different from the previous studies, the resulting group ring codes introduced by Hurleys are submodules and are ideals only in certain restrictive cases. Group ring codes introduced by Hurley are denoted as RG-codes where R is an integral domain and G is a group. In this thesis, we first study the family of F2G-codes where F2 is the finite field of order two, by viewing the codes as equivalent forms of some binary linear codes. A sufficient condition for a binary linear code to be equivalent to an F2Cn -code is determined. In addition to this, we start of the study of equivalence codes among F2G-codes by inventing a tool named group ring array. Triggered by an example of an F2D24 -code that is also an F2C24 -code up to equivalence, properties of F2Cn -codes as well as F2D2n -codes have been studied using group ring array. In particular, all F2D2n -codes for n 2,3,4,5 are exhibited thoroughly together with their respective generator and each is found to be equivalent to some F2C2n -codes. Lastly, a partial characterisation on the value of n with respect to when an F2D2n -code is equivalent to some F2C2n codes is established. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/3394 | |
| dc.subject | The idea of viewing cyclic codes as ideals | en_US |
| dc.subject | in cyclic group rings. | en_US |
| dc.title | Cyclic And Dihedral Group Ring Codes | en_US |
| dc.type | Thesis | en_US |
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