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## Locally recoverable codes from planar graphs

#### Kathryn HAYMAKER [1] , Justin O'PELLA [2]

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.
Error-correction, Local recovery, Planar graphs, Availability, Rate bound
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Primary Language en Engineering Articles Orcid: 0000-0001-5965-4197Author: Kathryn HAYMAKER (Primary Author) Orcid: 0000-0002-1381-4172Author: Justin O'PELLA Publication Date : February 29, 2020
 Bibtex @research article { jacodesmath645021, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {35 - 53}, doi = {10.13069/jacodesmath.645021}, title = {Locally recoverable codes from planar graphs}, key = {cite}, author = {Haymaker, Kathryn and O'pella, Justin} } APA Haymaker, K , O'pella, J . (2020). Locally recoverable codes from planar graphs . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (1) , 35-53 . DOI: 10.13069/jacodesmath.645021 MLA Haymaker, K , O'pella, J . "Locally recoverable codes from planar graphs" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 35-53 Chicago Haymaker, K , O'pella, J . "Locally recoverable codes from planar graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 35-53 RIS TY - JOUR T1 - Locally recoverable codes from planar graphs AU - Kathryn Haymaker , Justin O'pella Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.645021 DO - 10.13069/jacodesmath.645021 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 35 EP - 53 VL - 7 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.645021 UR - https://doi.org/10.13069/jacodesmath.645021 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Locally recoverable codes from planar graphs %A Kathryn Haymaker , Justin O'pella %T Locally recoverable codes from planar graphs %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 1 %R doi: 10.13069/jacodesmath.645021 %U 10.13069/jacodesmath.645021 ISNAD Haymaker, Kathryn , O'pella, Justin . "Locally recoverable codes from planar graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 1 (February 2020): 35-53 . https://doi.org/10.13069/jacodesmath.645021 AMA Haymaker K , O'pella J . Locally recoverable codes from planar graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 35-53. Vancouver Haymaker K , O'pella J . Locally recoverable codes from planar graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 35-53.

Authors of the Article
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