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.
Problems of Information Transmission – Springer Journals
Published: Jan 21, 2010
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