Locally Recoverable Codes From Planar Graphs

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Kathryn Haymaker¹  Justin O'Pella² 

[1] Department of Mathematics and Statistics, Villanova University, United States;Thomas Jefferson University, United States

关键词: Error-correction;    Local recovery;    Planar graphs;    Availability;    Rate bound;   

DOI  :  10.13069/jacodesmath.645021

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

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.

【 授权许可】

CC BY