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Axioms

Polycyclic Codes and Their Application in Constructing AEAQECCs

Juan Li, Yunbo Tian, Fanghui Ma

Published Feb 2, 2026• 0 citations
Publisher

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.

DOI
10.3390/axioms15020110

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