Johnson Graph Codes
Combinatorics
2019-12-24 v1 Information Theory
math.IT
Abstract
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.
Keywords
Cite
@article{arxiv.1912.10388,
title = {Johnson Graph Codes},
author = {Iwan Duursma and Xiao Li},
journal= {arXiv preprint arXiv:1912.10388},
year = {2019}
}
Comments
33 pages