On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings
Abstract
:1. Introduction
2. Preliminary Results
- (i)
- The Hamming distance between two vectors and is the number of places where they differ, and is denoted by .
- (ii)
- The Hamming weight of a vector is the number of non-zero and is denoted by .
- (iii)
- The Euclidean inner product of any two vectors and is defined as and the dual of linear code is .
- (iv)
- A code is said to be self-dual if , self-orthogonal if , and dual containing if .
3. Structural Properties of Cyclic Codes over R
4. Quantum and LCD Codes
5. Applications
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Ali, S.; Alali, A.S.; Jeelani, M.; Kurulay, M.; Öztas, E.S.; Sharma, P. On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings. Axioms 2023, 12, 367. https://doi.org/10.3390/axioms12040367
Ali S, Alali AS, Jeelani M, Kurulay M, Öztas ES, Sharma P. On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings. Axioms. 2023; 12(4):367. https://doi.org/10.3390/axioms12040367
Chicago/Turabian StyleAli, Shakir, Amal S. Alali, Mohammad Jeelani, Muhammet Kurulay, Elif Segah Öztas, and Pushpendra Sharma. 2023. "On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings" Axioms 12, no. 4: 367. https://doi.org/10.3390/axioms12040367