Everts, A.R.F.
(2009)
Automorphism groups of cyclic codes.
Bachelor's Thesis, Mathematics.
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: |
| Supervisor name | Supervisor E mail |
|---|
| Top, J. | UNSPECIFIED |
|
| 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: |
http://fse.studenttheses.ub.rug.nl/id/eprint/8609 |
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