Locally Recoverable Codes From Planar Graphs

Authors

Kathryn Haymaker, Villanova University
Justin O'Pella, Thomas Jefferson UniversityFollow

Document Type

Article

Publication Date

1-15-2020

Comments

This article is the author’s final published version in Journal of Algebra Combinatorics Discrete Structures and Applications, Volume 7, Issue 1, January 2020, Pages 35–53.

The published version is available at https://doi.org/0.13069/jacodesmath.645021. Copyright © Haymaker & O'Pella

Abstract

In this paper we apply Kadhe and Calderbank’s definition of LRCs from convex polyhedra and planar graphs [4] 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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Haymaker, Kathryn and O'Pella, Justin, "Locally Recoverable Codes From Planar Graphs" (2020). Kanbar College Faculty Papers. Paper 3.
https://jdc.jefferson.edu/kanbarfp/3

Language

English