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In this paper, we construct higher-order generalizations of the $A_6^{(1)}$-and $A_4^{(1)}$-surface type $q$-Painlev\'e equations from the system ofpartial difference equations with the consistency around a cube property byperiodic reduction. Moreover, we also show their extended affine Weyl groupsymmetries and Lax pairs.

Higher-order generalizations of the $A_6^{(1)}$- and $A_4^{(1)}$-surface type $q$-Painlev\'e equations