Everts, A.R.F. (2009) Automorphism groups of cyclic codes. Bachelor's Thesis, Mathematics.
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Abstract
Codes are used to store and send information. In this thesis we discuss binary codes, which can be seen as subsets of F_2^n. Permuting the coordinates of a code results in an equivalent code, which shares a lot of the same properties with the original code. The automorphism group of a binary code consists of all permutations that map a code back to itself. An automorphism group of a code gives information about the structure of the code, but it is difficult to determine. In this thesis we prove that the automorphism group of the Hamming code of length n = 2^m -1 is isomorphic to GL m,2). Next, we consider some transitive subgroups of S_n and discuss whether they can occur as an automorphism group of a cyclic code of length n. We also give an application of automorphism groups to the minimum weight of a code. In the last chapter, we use coding theory to prove a theorem about permutation groups.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:28 |
| Last Modified: | 17 Apr 2019 12:43 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/8609 |
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