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Automorphism groups of cyclic codes

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:
Supervisor nameSupervisor 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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