Affine $3$-nonsystematic codes

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.