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Construction of Quantum Codes over the Class of Commutative Rings and Their Applications to DNA Codes

Author

Listed:
  • Shakir Ali

    (Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India)

  • Amal S. Alali

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Elif Segah Oztas

    (Department of Mathematics, Kamil Ozdag Science Faculty, Karamanoglu Mehmetbey University, Karaman 70100, Türkiye)

  • Pushpendra Sharma

    (Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India)

Abstract

Let k , m be positive integers and F 2 m be a finite field of order 2 m of characteristic 2. The primary goal of this paper is to study the structural properties of cyclic codes over the ring S k = F 2 m [ v 1 , v 2 , … , v k ] ⟨ v i 2 − α i v i , v i v j − v j v i ⟩ , for i , j = 1 , 2 , 3 , … , k , where α i is the non-zero element of F 2 m . As an application, we obtain better quantum error correcting codes over the ring S 1 (for k = 1 ). Moreover, we acquire optimal linear codes with the help of the Gray image of cyclic codes. Finally, we present methods for reversible DNA codes.

Suggested Citation

  • Shakir Ali & Amal S. Alali & Elif Segah Oztas & Pushpendra Sharma, 2023. "Construction of Quantum Codes over the Class of Commutative Rings and Their Applications to DNA Codes," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1430-:d:1098491
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