Construction of Hermitian Self-Orthogonal Codes and Application
Abstract
:1. Introduction
2. Preliminaries
- (1)
- is an HSO code if and only if .
- (2)
- is a HLCD code if and only if is nonsingular.
- (1)
- If is an HSO block, . Then, and generates an HSO code.
- (2)
- If is an HLCD block, and . Then, , generates an HLCD code.
3. Constructing HSO Codes
3.1. HSO Codes for
- (1)
- for ;
- (2)
- for and .
- (1)
- for ;
- (2)
- for and ;
- (3)
- for ;
- (4)
- for and .
3.2. HSO Codes for
- (1)
- for , and for and ;
- (2)
- for , and for and ;
- (3)
- for , and for and ;
- (4)
- for , and for and .
4. Construction of HLCD Codes
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
HSO | Hermitian self-orthogonal |
HLCD | Hermitian linear complementary dual |
EAQECC | Entanglement-assisted quantum error-correcting code |
Appendix A. Generator Matrices of Some Special Optimal HSO Codes
Appendix A.1. Generator matrices G 5,386 and G 5,407 in Section 3.1
Appendix A.2. Generator Matrices G5,172, G5,194, G5,215, and G5,236 in Section 3.2
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Ren, Y.; Li, R.; Song, H. Construction of Hermitian Self-Orthogonal Codes and Application. Mathematics 2024, 12, 2117. https://doi.org/10.3390/math12132117
Ren Y, Li R, Song H. Construction of Hermitian Self-Orthogonal Codes and Application. Mathematics. 2024; 12(13):2117. https://doi.org/10.3390/math12132117
Chicago/Turabian StyleRen, Yuezhen, Ruihu Li, and Hao Song. 2024. "Construction of Hermitian Self-Orthogonal Codes and Application" Mathematics 12, no. 13: 2117. https://doi.org/10.3390/math12132117
APA StyleRen, Y., Li, R., & Song, H. (2024). Construction of Hermitian Self-Orthogonal Codes and Application. Mathematics, 12(13), 2117. https://doi.org/10.3390/math12132117