In this paper, we study the properties that an output feedback matrix over a finite field, \(K \in \mathbb {F}_{q}^{k \times (n-k)}\) , must satisfy to preserve some structural properties of the associated output feedback system. Our aim is to use these conditions to construct (n, k)-convolutional codes with optimal properties of observability and decoding via their linear associated dynamical systems or input/state/output representations. Thus, we derive explicit algebraic conditions under which output feedback preserves reachability, observability, and invertibility of the state matrix. Our approach is constructive, applying output feedback while simultaneously modifying the external signal space, thereby potentially producing new convolutional codes. Also, we derive explicit lower bounds on the proportion of admissible output feedback matrices that maintain the desired properties.