Quantum Codes as an Application of Constacyclic Codes
The main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring R=Fp+w1Fp+w2Fp+w22Fp+w1w2Fp+w1w22Fp, where w12−α2=0, w1w2=w2w1, w23−β2w2=0, and α,β∈Fp∖{0}, for a prime p. We begin by introducing a Gray map defined over R, which is associated with an invertible matrix. We demonstrate its advantages over the canonical Gray map through some examples. Finally, we create new and improved quantum codes from constacyclic codes over R using Calderbank–Shore–Steane (CSS) construction.
Authors
- Mohammad Fareed Ahmad
- Nadeem ur Rehman (ORCID: https://orcid.org/0000-0003-3955-7941)
- Abdul Nadim Khan (ORCID: https://orcid.org/0000-0002-5861-6137)
- Patrick Solé (ORCID: https://orcid.org/0000-0002-4078-8301)
- Hatoon Shoaib (ORCID: https://orcid.org/0000-0002-1888-8154)
- Manish K. Gupta (ORCID: https://orcid.org/0000-0001-7067-8085)
- Adel Alahmadi
- Arif Raza (ORCID: https://orcid.org/0000-0001-6799-8969)
- Widyan Basaffar (ORCID: https://orcid.org/0000-0003-1639-9186)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Aligarh Muslim University (IN)
- King Abdulaziz University (SA)
- Aix-Marseille Université (FR)
- Centrale Méditerranée (FR)
- Institut Polytechnique de Bordeaux (FR)
Publication Details
- Journal
- Axioms
- Published
- 2024-10-08
- DOI
- https://doi.org/10.3390/axioms13100697
- Citations
- 1
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 0.35
Funders
- King Abdulaziz University