Totally synchronizing generated system

‎‎We introduce the notion of a minimal generator $G$ for the coded system $X$; that is a generator for coded system $X$ whenever $u \in G$‎, ‎then $u \not \in W(\overline{})$‎. ‎Such an $X$ is called \emph{minimally‎ ‎generated system}‎. ‎We ‎aim ‎to‎ introduce a class of minimally‎ ‎generated subshifts generated by some certain synchronizing blocks‎. ‎These systems are precisely the tool that will enable us to show that for such subshifts $X$‎, ‎each $x \in X$‎‎ can be written uniquely as‎ $x=\ldots v_{-1}v_{0}v_1v_2\ldots$, where $\{\ldots‎ ,‎v_{-1},v_{0},v_1,v_2,\ldots\}\in G$.‎‎‎‎‎‎ ‎Shows that the converse of that proposition isn't necessarily true‎.‎ {\color{red}‎ ‎‎‎‎‎‎We will show which of the components of the Kreiger graph of such a subshift could be a candidate to be suitable for a Fischer cover‎.‎‎‎‎‎ }