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In this paper, we investigate the algebraic structure for polycyclic codes over a specific class of serial rings, defined as R=Rx₁, , xₛ/ t₁ (x₁), , tₛ (xₛ), where R is a chain ring and each tᵢ (xᵢ) in Rxᵢ for i\1, , s\ is a monic square-free polynomial. We define quasi-s-dimensional polycyclic codes and establish an R-isomorphism between these codes and polycyclic codes over R. We provide necessary and sufficient conditions for the existence of annihilator self-dual, annihilator self-orthogonal, annihilator linear complementary dual, and annihilator dual-containing polycyclic codes over this class of rings. We also establish the CSS construction for annihilator dual-preserving polycyclic codes over the chain ring R and use this construction to derive quantum codes from polycyclic codes over R.
Bajalan et al. (Tue,) studied this question.