Johnson Graph Codes
| Autor: | Iwan Duursma, Xiao Li |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Computer Science::Emerging Technologies Computer Science - Information Theory Applied Mathematics Information Theory (cs.IT) FOS: Mathematics Mathematics - Combinatorics Data_CODINGANDINFORMATIONTHEORY Combinatorics (math.CO) Computer Science Applications MathematicsofComputing_DISCRETEMATHEMATICS |
| DOI: | 10.48550/arxiv.1912.10388 |
| Popis: | We define a Johnson graph code as a subspace of labelings of the vertices in a Johnson graph with the property that labelings are uniquely determined by their restriction to vertex neighborhoods specified by the parameters of the code. We give a construction and main properties for the codes and show their role in the concatenation of layered codes that are used in distributed storage systems. A similar class of codes for the Hamming graph is discussed in an appendix. Codes of the latter type are in general different from affine Reed-Muller codes, but for the special case of the hypercube they agree with binary Reed-Muller codes. Comment: 33 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|