Polycyclic Codes over Serial Rings: Algebraic Structure and Annihilator CSS Construction

This paper investigates the algebraic structure of polycyclic codes over a specific class of serial rings, defined as R = R[x1, ..., xs]/⟨t1(x1), ..., ts(xs)⟩, where R is a chain ring and each ti(xi) is a monic square-free polynomial. It provides necessary and sufficient conditions for the existence of various types of annihilator dual polycyclic codes over this class of rings and establishes an annihilator CSS construction to derive quantum codes from annihilator dual-preserving polycyclic codes.