Affine $3$-nonsystematic perfect codes of length 15

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.