Locally recoverable codes from planar graphs

Year 2020, Volume: 7 Issue: 1 (Special Issue in Algebraic Coding Theory: New Trends and Its Connections), 35 - 53, 29.02.2020

Kathryn Haymaker Justin O'pella

https://doi.org/10.13069/jacodesmath.645021

Abstract

In this paper we apply Kadhe and Calderbank's definition of LRCs from convex polyhedra and planar graphs \cite{KAD} to analyze the codes resulting from 3-connected regular and almost regular planar graphs. The resulting edge codes are locally recoverable with availability two. We prove that the minimum distance of planar graph LRCs is equal to the girth of the graph, and we also establish a new bound on the rate of planar graph edge codes. Constructions of regular and almost regular planar graphs are given, and their associated code parameters are determined. In certain cases, the code families meet the rate bound.

Keywords

Error-correction, Local recovery, Planar graphs, Availability, Rate bound

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