Automorphism groups of cyclic codes
Rolf Bienert
and Benjamin Klopsch
DOI: 10.1007/s10801-009-0179-y
Abstract
In this article we study the automorphism groups of binary cyclic codes. In particular, we provide explicit constructions for codes whose automorphism groups can be described as (a) direct products of two symmetric groups or (b) iterated wreath products of several symmetric groups. Interestingly, some of the codes we consider also arise in the context of regular lattice graphs and permutation decoding.
Pages: 33–52
Keywords: keywords binary cyclic codes; automorphism groups
Full Text: PDF
References
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2. Bienert, R.: Über Automorphismengruppen von zyklischen Codes. Dissertation, Heinrich-Heine- Universität (2007)
3. Huffman, W.C.: Codes and groups. In: Handbook of Coding Theory, vol. II, pp. 1345-1440. North- Holland, Amsterdam (1998)
4. Jones, G.: Cyclic regular subgroups of primitive permutation groups. J. Group Theory 5, 403-407 (2002)
5. Key, J.D., Seneviratne, P.: Binary codes from rectangular lattice graphs and permutation decoding. European J. Combin. 28, 121-126 (2007)
6. Kantor, W.M., McDonough, T.P.: On the maximality of PSL(d + 1, q), d \geq
2. J. London Math. Soc. 8, 426 (1974)
7. Knapp, W., Schmid, P.: Codes with prescribed permutation group. J. Algebra 67, 415-435 (1980)
8. Mortimer, B.: The modular permutation representations of the known doubly transitive groups. Proc. London Math. Soc. 41, 1-20 (1980)
9. Phelps, K.T.: Every finite group is the automorphism group of some linear code. Congr. Numer. 49, 139-141 (1985). Proceedings of the Sixteenth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, Fl., 1985)
10. Wiegold, J., Williamson, A.G.: The factorisation of the alternating and symmetric groups. Math. Z.