Geodesic
The automorphism group of a~$q$-ary Hamming code
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 6, pp. 50-55.

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It is well known that the semilinear symmetry group of a $q$-ary Hamming code $\mathcal H$ with length $n=\frac{q^m-1}{q-1}$ is isomorphic to $\mathit\Gamma L_m(q)$. This does not clarify if all symmetries of the code are semilinear or not. Here we prove that each symmetry of the code constituted by all triples in $\mathcal H$ is semilinear. This implies that every symmetry of the Hamming code is semilinear. So, it is shown that the automorphism group of a $q$-ary Hamming code is isomorphic to the semidirect product $\mathit\Gamma L_m(q)\rightthreetimes\mathcal H$. Bibliogr. 4.
Keywords: the Hamming code
Mots-clés : automorphism group. 
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E. V. Gorkunov. The automorphism group of a~$q$-ary Hamming code. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 6, pp. 50-55. http://geodesic.mathdoc.fr/item/DA_2010_17_6_a2/

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