${\mathsf{\text{𝖦𝖫𝖾𝗏}}}_{S,\sigma }^{\beta ,l}(M)={\left\{{\mathsf{\text{𝖦𝖫𝖶𝖤}}}_{S,\sigma }\left({\displaystyle \frac{q}{{\beta }^i}}M+E_i\right)\right\}}_{i=1}^l\in R_{⟨n,q⟩}^{(k+1)\cdot l}$