Counting double-polycyclic codes over a finite chain ring of nilpotency index two

In this paper, we study the algebraic structure of double-polycyclic codes over a finite chain ring $ R $ with a nilpotency index of two, defined by associated square-free polynomials. We also provide formulas for the number of separable and non-separable double-polycyclic codes. Finally, we briefly discuss the number of non-separable $ \mathbb{F}_q R $-polycyclic codes, where $ \mathbb{F}_q $ is the residue field of $ R $.