Geodesic
On transitive uniform partitions of $F^n$ into binary Hamming codes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 886-892

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We investigate transitive uniform partitions of the vector space $F^n$ of dimension $n$ over the Galois field $GF(2)$ into cosets of Hamming codes. A partition $P^n= \{H_0,H_1+e_1,\ldots,H_n+e_n\}$ of $F^n$ into cosets of Hamming codes $H_0,H_1,\ldots,H_n$ of length $n$ is said to be uniform if the intersection of any two codes $H_i$ and $H_j$, $i,j\in \{0,1,\ldots,n \}$ is constant, here $e_i$ is a binary vector in $F^n$ of weight $1$ with one in the $i$th coordinate position. For any $n=2^m-1$, $m>4$ we found a class of nonequivalent $2$-transitive uniform partitions of $F^n$ into cosets of Hamming codes.
Keywords: Hamming code, uniform partition into Hamming codes, Reed–Muller code, dual code.
Mots-clés : partition, transitive partition, $2$-transitive partition 
@article{SEMR_2019_16_a90,
     author = {F. I. Solov'eva},
     title = {On transitive uniform partitions of $F^n$ into binary {Hamming} codes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {886--892},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a90/}
}
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F. I. Solov'eva. On transitive uniform partitions of $F^n$ into binary Hamming codes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 886-892. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a90/