Cyclic LRCs with Availability from Linearized Polynomials

Zhengchun ZHOU
Haode YAN

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E104-A    No.7    pp.991-995
Publication Date: 2021/07/01
Publicized: 2021/01/18
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020EAL2100
Type of Manuscript: LETTER
Category: Coding Theory
locally repairable codes,  distributed storage systems,  availability,  repair locality,  multiple failures,  

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Locally repairable codes (LRCs) with availability have received considerable attention in recent years since they are able to solve many problems in distributed storage systems such as repairing multiple node failures and managing hot data. Constructing LRCs with locality r and availability t (also called (r, t)-LRCs) with new parameters becomes an interesting research subject in coding theory. The objective of this paper is to propose two generic constructions of cyclic (r, t)-LRCs via linearized polynomials over finite fields. These two constructions include two earlier ones of cyclic LRCs from trace functions and truncated trace functions as special cases and lead to LRCs with new parameters that can not be produced by earlier ones.