Generalized Singleton Type Upper Bounds
- Resource Type
- Periodical
- Authors
- Chen, H.; Qu, L.; Li, C.; Lyu, S.; Xu, L.; Zhou, M.
- Source
- IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 70(5):3298-3308 May, 2024
- Subject
- Communication, Networking and Broadcast Technologies
Signal Processing and Analysis
Codes
Upper bound
Linear codes
Reed-Solomon codes
Measurement
Hamming weight
Hamming distances
Covering code
generalized singleton type upper bound
symbol-pair code
insertion-deletion code
singleton-optimal locally recoverable code
- Language
- ISSN
- 0018-9448
1557-9654
In this paper, we give many new Singleton type upper bounds on the sizes of codes with given minimum Hamming distances. These upper bounds are stronger than the Griesmer bound when the lengths of codes are large. Some upper bounds on the lengths of general small Singleton defect codes are presented. Our generalized Singleton type upper bounds have wide applications to symbol-pair codes, insertion-deletion codes and locally recoverable codes. The generalized Singleton type upper bounds on symbol-pair codes and insertion-deletion codes are much stronger than the direct Singleton bounds on symbol-pair codes and insertion-deletion codes when the lengths are large and the Hamming minimum distances are small. Upper bounds on the lengths of small dimension optimal locally recoverable codes and small dimension optimal $(r, \delta)$ locally recoverable codes with any given minimum distance are also presented.