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arXiv · 1912.10388

Johnson Graph Codes

Iwan Duursma·Xiao Li
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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.

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Iwan Duursma, Xiao Li. 2019-12-22. Johnson Graph Codes. https://arxiv.org/abs/1912.10388

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