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

08/14/2018

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by   Lingfei Jin, et al.

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It was shown in GXY18 that the length n of a q-ary linear locally recoverable code with distance d> 5 is upper bounded by O(dq^3). 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 GXY18 also gave an algorithmic construction of q-ary locally recoverable codes with locality r and length n=Ω_r(q^2) 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 GXY18.