Year: 2026
Type: article
Abstract: In this article, we study polycyclic codes over the ring R=Fq[v]/⟨v2−1⟩, where q=pm with p being an odd prime. First, we introduce polycyclic codes and sequential codes over R, and characterize the structural properties of these polycyclic codes. Next, we analyze the Euclidean dual codes, annihilator dual codes, annihilator self-orthogonal codes, and annihilator linear complementary dual (LCD) codes associated with this family of codes. Finally, some asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) are constructed from polycyclic codes over R. Moreover, the parameters of our AEAQECCs are new in the existing literature.
Source: Axioms
Authors: Juan Li, Yunbo Tian, Fanghui Ma
Institutions: Linyi University, Shandong University of Technology
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Awards: G4443088662, G6048621918
OpenAlex ID: W7127084752