Geodesic
On nonsystematic perfect codes over finite fields
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 1, pp. 44-63

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Nonsystematic perfect $q$-ary codes over a field $F_q$ of length $n=(q^m-1)/(q-1)$ are constructed for $m\ge4$ and $q\ge2$, and also for $n=3$ and non prime $q$. It is shown that, for $q\ne3,5$, such codes can be constructed by switchings seven disjoint components and, for $q=3,5$, by switchings eight disjoint components of the Hamming code $H_q^n$. Bibl. 12.
Keywords: perfect code, Hamming code, Galois field, nonsystematic code, projective geometry, component. 
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     author = {S. A. Malyugin},
     title = {On nonsystematic perfect codes over finite fields},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/DA_2009_16_1_a2/}
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S. A. Malyugin. On nonsystematic perfect codes over finite fields. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 1, pp. 44-63. http://geodesic.mathdoc.fr/item/DA_2009_16_1_a2/