Geodesic
Affine $3$-nonsystematic codes
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 4, pp. 54-61

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A perfect binary code $C$ of length $n=2^k-1$ is called affine $3$-systematic if in the space $\{0,1\}^n$ there exists a $3$-dimensional subspace $L$ such that the intersection of any of its cosets $L+u$ with the code $C$ is either empty or a singleton. Otherwise, the code $C$ is called affine $3$-nonsystematic. We construct affine $3$-nonsystematic codes of length $n=2^k-1$, $k\geq4$. Bibliogr. 11.
Keywords: perfect code, Hamming code, nonsystematic code, affine nonsystematic code, affine $3$-nonsystematic code, component. 
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     author = {S. A. Malyugin},
     title = {Affine $3$-nonsystematic codes},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {54--61},
     publisher = {mathdoc},
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     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2014_21_4_a5/}
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S. A. Malyugin. Affine $3$-nonsystematic codes. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 4, pp. 54-61. http://geodesic.mathdoc.fr/item/DA_2014_21_4_a5/