Quantum Codes as an Application of Constacyclic Codes
Mohd Arif Raza,
Mohammad Fareed Ahmad,
Adel Alahmadi,
Widyan Basaffar,
Manish K. Gupta,
Nadeem ur Rehman,
Abdul Nadim Khan,
Hatoon Shoaib,
Patrick Sole
Affiliations
Mohd Arif Raza
Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science & Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia
Mohammad Fareed Ahmad
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Adel Alahmadi
Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Widyan Basaffar
Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Manish K. Gupta
Director Academics Office, Kaushalya: The Skill University, Ahmedabad 382424, India
Nadeem ur Rehman
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Abdul Nadim Khan
Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science & Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia
Hatoon Shoaib
Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Patrick Sole
I2M, (CNRS, Aix-Marseille University, Centrale Marseille), 163 Avenue de Luminy, 13009 Marseilles, France
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.
