Geodesic
A note on regular subgroups of the automorphism group of the linear Hadamard code
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1455-1462

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We consider the subgroups of the automorphism group of the linear Hadamard code that act regularly on the codewords of the code. These subgroups correspond to the regular subgroups of the general affine group $\mathrm{GA}(r,2)$ with respect to the action on the vectors of $F_2^{r}$, where $n=2^r-1 $ is the length of the Hamadard code. We show that the dihedral group $D_{2^{r-1}}$ is a regular subgroup of $\mathrm{GA}(r,2)$ only when $r=3$. Following the approach of [13] we study the regular subgroups of the automorphism group of the Hamming code obtained from the regular subgroups of the automorphism group of the Hadamard code of length $15$.
Keywords: error-correcting code, regular action
Mots-clés : automorphism group, affine group. 
@article{SEMR_2018_15_a80,
     author = {I. Yu. Mogilnykh},
     title = {A note on regular subgroups of the automorphism group of the linear {Hadamard} code},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1455--1462},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a80/}
}
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I. Yu. Mogilnykh. A note on regular subgroups of the automorphism group of the linear Hadamard code. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1455-1462. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a80/