Locally Repairable Codes from Cyclic Codes and Generalized Quadrangles

Qiang FU  Ruihu LI  Luobin GUO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.7   pp.947-950
Publication Date: 2020/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAL2170
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
repair locality,  availability,  cyclic code,  generalized quadrangle,  

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Summary: 
Locally repairable codes (LRCs) with locality r and availability t are a class of codes which can recover data from erasures by accessing other t disjoint repair groups, that every group contain at most r other code symbols. This letter will investigate constructions of LRCs derived from cyclic codes and generalized quadrangle. On the one hand, two classes of cyclic LRC with given locality m-1 and availability em are proposed via trace function. Our LRCs have the same locality, availability, minimum distance and code rate, but have short length and low dimension. On the other hand, an LRC with $(2,(p+1)lfloor rac{s}{2} floor)$ is presented based on sets of points in PG(k, q) which form generalized quadrangles with order (s, p). For k=3, 4, 5, LRCs with r=2 and different t are determined.