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Perfect codes and related structures / Tuvi Etzion
Material type:
TextLanguage: English Publication details: Singapore : World scientific Publishing Company Pvt. Ltd, 2022.Description: 421 p. ; 15.9 cmISBN: - 9789811255878
- 003.54 ETZ
Contents:
Summary: This monograph provides a comprehensive exploration of perfect codes and related structures within coding theory. It delves into the mathematical properties of these codes, including their largest possible size and their behavior in various metrics. The book covers a wide range of topics, such as diameter perfect codes, quasi-perfect codes, and combinatorial designs, offering a diverse perspective on the field. By presenting new constructions and deriving bounds on code sizes, the book contributes to ongoing research in coding theory and provides valuable insights for both researchers and students.
1. Codes, Block Length, Code Rate
2. Hamming Distance, Minimum Distance
3. Error-Correcting and Error-Detecting Capabilities
4. Linear Codes
5. Generator and Parity-Check Matrices
6. Hamming Codes
7. Cyclic Codes
8. BCH Codes
9. Reed-Solomon Codes
10. Perfect Codes in Hamming Metric
11. Sphere-Packing Bound
12. Generalized Hamming Codes
13. Golay Codes
14. Perfect Codes in Johnson Metric
15. Perfect Codes in Lee Metric
16. Perfect Codes in Grassmann Metric
17. Diameter Perfect Codes
18. Quasi-Perfect Codes
19. Mixed Codes
20. Tilings and Combinatorial Designs
21.Open Problems and Future Directions
| Item type | Current library | Collection | Shelving location | Call number | Status | Barcode | |
|---|---|---|---|---|---|---|---|
Reference
|
Kalaignar Centenary Library Madurai | ENGLISH-REFERENCE BOOKS | நான்காம் தளம் / Fourth floor | 003.54 ETZ (Browse shelf(Opens below)) | Not for loan | 105728 |
Includes bibliography.
1. Codes, Block Length, Code Rate
2. Hamming Distance, Minimum Distance
3. Error-Correcting and Error-Detecting Capabilities
4. Linear Codes
5. Generator and Parity-Check Matrices
6. Hamming Codes
7. Cyclic Codes
8. BCH Codes
9. Reed-Solomon Codes
10. Perfect Codes in Hamming Metric
11. Sphere-Packing Bound
12. Generalized Hamming Codes
13. Golay Codes
14. Perfect Codes in Johnson Metric
15. Perfect Codes in Lee Metric
16. Perfect Codes in Grassmann Metric
17. Diameter Perfect Codes
18. Quasi-Perfect Codes
19. Mixed Codes
20. Tilings and Combinatorial Designs
21.Open Problems and Future Directions
This monograph provides a comprehensive exploration of perfect codes and related structures within coding theory. It delves into the mathematical properties of these codes, including their largest possible size and their behavior in various metrics. The book covers a wide range of topics, such as diameter perfect codes, quasi-perfect codes, and combinatorial designs, offering a diverse perspective on the field. By presenting new constructions and deriving bounds on code sizes, the book contributes to ongoing research in coding theory and provides valuable insights for both researchers and students.