Geodesic
Affine $3$-nonsystematic perfect codes of length 15
Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 1, pp. 32-50 Cet article a éte moissonné depuis la source Math-Net.Ru

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A perfect binary code $C$ of length $n=2^k-1$ is called affine $3$-systematic if there exists a $3$-dimensional subspace $L$ in the space $\{0,1\}^n$ such that the intersection of any of its cosets $L+u$ with $C$ is either empty, or a singleton. Otherwise, the code $C$ is called affine $3$-nonsystematic. In the paper, we construct four nonequivalent affine $3$-nonsystematic codes of length 15. Bibliogr. 12.
Keywords: perfect code, Hamming code, nonsystematic code, affine nonsystematic code, affine $3$-nonsystematic code, component. 
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S. A. Malyugin. Affine $3$-nonsystematic perfect codes of length 15. Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 1, pp. 32-50. http://geodesic.mathdoc.fr/item/DA_2015_22_1_a2/

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