New Quantum Codes Derived from Constacyclic Structures

Researchers have constructed a new class of entanglement-assisted quantum error-correcting codes, known as EAQECCs, via the Gray images of constacyclic codes over a finite non-chain ring. The newly constructed class of quantum codes also includes certain maximal entanglement codes, formally designated as ME-EAQECCs.

The underlying mathematical framework of this construction relies on the algebraic ring R, defined as the quotient ring of the polynomial ring in variable v over the finite field F_q modulo the ideal generated by the polynomial v cubed minus v. Within this algebraic setting, the parameter q is specified as an odd prime power, establishing R as a finite non-chain ring. The authors construct constacyclic codes over this specific ring R and subsequently transform them into EAQECCs by determining their Gray images.

To demonstrate the concrete effectiveness of this theoretical construction, the authors present several explicit code examples within the publication.

In direct performance evaluations, the parameters of the codes constructed in this research are superior to those of the known EAQECCs provided in reference [1].

Subject of Research: Construction of entanglement-assisted quantum error-correcting codes from constacyclic codes over finite non-chain rings

Article Title: EAQECCs from constacyclic codes over the finite non-chain ring \(\mathbb {F}_{q}[v]/\langle v^3-v\rangle \)

Article References: Li, J., Tian, Y., & Ma, F. (2026). EAQECCs from constacyclic codes over the finite non-chain ring $$\mathbb {F}_{q}[v]/\langle v^3-v\rangle $$. Quantum Information Processing, 25(11), Article 359. https://doi.org/10.1007/s11128-026-05396-7

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DOI: 10.1007/s11128-026-05396-7

Keywords: quantum error correction, constacyclic codes, finite rings, quantum information, entanglement-assisted codes, algebraic coding theory, Gray images, quantum communication, EAQECCs, constacyclic, codes, over