The group of permutation automorphisms of a q-ary hamming code

The group of permutation automorphisms of a q-ary hamming code We prove that the group of permutation automorphism of a q-ary Hamming code of length n = (q m − 1)/(q − 1) is isomorphic to the unitriangular group UT m (q) if the code has a parity-check matrix composed of all columns of the form (0 ...0 1 * ... *)T. We also show that the group of permutation automorphisms of a cyclic Hamming code cannot be isomorphic to UT m (q). We thus show that equivalent codes can have different permutation automorphism groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

The group of permutation automorphisms of a q-ary hamming code

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946009040024
Publisher site
See Article on Publisher Site

Abstract

We prove that the group of permutation automorphism of a q-ary Hamming code of length n = (q m − 1)/(q − 1) is isomorphic to the unitriangular group UT m (q) if the code has a parity-check matrix composed of all columns of the form (0 ...0 1 * ... *)T. We also show that the group of permutation automorphisms of a cyclic Hamming code cannot be isomorphic to UT m (q). We thus show that equivalent codes can have different permutation automorphism groups.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 21, 2010

References

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