Geodesic
Affine $3$-nonsystematic perfect codes of length~15
Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 1, pp. 32-50

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DA_2015_22_1_a2,
     author = {S. A. Malyugin},
     title = {Affine $3$-nonsystematic perfect codes of length~15},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {32--50},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2015_22_1_a2/}
}
TY  - JOUR
AU  - S. A. Malyugin
TI  - Affine $3$-nonsystematic perfect codes of length~15
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2015
SP  - 32
EP  - 50
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2015_22_1_a2/
LA  - ru
ID  - DA_2015_22_1_a2
ER  - 
%0 Journal Article
%A S. A. Malyugin
%T Affine $3$-nonsystematic perfect codes of length~15
%J Diskretnyj analiz i issledovanie operacij
%D 2015
%P 32-50
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2015_22_1_a2/
%G ru
%F DA_2015_22_1_a2
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/