Explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes

2018/08/14 by Jin, Lingfei · 4 citations
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1808.04558

Abstract

It was shown in \citeGXY18 that the length n of a q-ary linear locally recoverable code with distance d≥ 5 is upper bounded by O(dq³). Thus, it is a challenging problem to construct q-ary locally recoverable codes with distance d≥ 5 and length approaching the upper bound. The paper \citeGXY18 also gave an algorithmic construction of q-ary locally recoverable codes with locality r and length n=Ω_r(q²) for d=5 and 6, where Ω_r means that the implicit constant depends on locality r. In the present paper, we present an explicit construction of q-ary locally recoverable codes of distance d= 5 and 6 via binary constant weight codes. It turns out that (i) our construction is simpler and more explicit; and (ii) lengths of our codes are larger than those given in \citeGXY18.

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