2024/04/16 by Maryam Bajalan, Bajalan, Maryam, Edgar Martı́nez-Moro +1
Computer Science · Engineering · Social Sciences · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Islamic Finance and Communication #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2404.10452
openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the algebraic structure for polycyclic codes over a specific class of serial rings, defined as \mathscr R=R[x1,…, xs]/⟨ t1(x1),…, ts(xs) ⟩, where R is a chain ring and each ti(xi) in R[xi] 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 \mathscr 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 \mathscrR.