  q-ary cumulative-separable $\Gamma(L,G^{(j)})$-codes $L=\{ \alpha \in
GF(q^{m}):G(\alpha )\neq 0 \}$ and $G^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q$ are
considered. The relation between different codes from this class is
demonstrated. Improved boundaries of the minimum distance and dimension are
obtained.
