ϒ – Constacyclic codes over a Frobenius ring and their application to find novel quantum codes

Soni, Pooja; Pruthi, Manju; Yadav, Arun Kumar

doi:10.47974/JDMSC-2415

Open Access Research Article

ϒ – Constacyclic codes over a Frobenius ring and their application to find novel quantum codes

^*Pooja SoniCorresponding authorpooja.math.rs@igu.ac.inDepartment of MathematicsMeerpurIndira Gandhi UniversityRewari, Haryana, 123401, IndiaView full profile → , Manju Pruthimanju.pruthi@yahoo.comDepartment of MathematicsMeerpurIndira Gandhi UniversityRewari, Haryana, 123401, IndiaView full profile → , Arun Kumar Yadavarun.math.rs@igu.ac.inSchool of Basic and Applied SciencesSohna RoadK. R. Mangalam UniversityGurugram, Haryana, 122103, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 229–241Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2415 Crossmark XML

Received:: 11 Feb 2025
Published Online:: 30 Dec 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2415
Pages:: 229–241

Abstract

In this work, we use the Hermitian technique to find novel Quantum error correcting codes (𝒬E𝒞𝒞’s) by Constacyclic codes (CCc’s) over the ring ℛ = ℱp2 [𝓊, 𝓋]/(𝓊3 – ω2 𝓊, 𝓋3 – ω2 𝓋), where p is a non-even prime power and ℱ*p2 = ⟨ω⟩. Firstly, we express the ring in terms of “pairwise orthogonal Idempotent” elements & analyze “linear codes.” We investigate ring structure and establish a one-one, onto and distance preserving Gray map, ∅ ∶ ℛ𝓃→ℱ5𝓃p2. We provide the units of ℛ, to analyze CCc’s & their generators. We also give a condition for this code to contain its Hermitian dual over ℛ. At last, we derive and tabulate some novel and efficient 𝒬E𝒞𝒞’s.

Keywords

𝒬E𝒞𝒞 Hermitian CCc Gray map

Subject Classifications

94B0594B1594B35

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