Optimal (r,δ)-locally repairable codes decompose into MDS local codes, forcing d≥δ, and this structure yields new optimal quantum (r,δ)-LRCs.
Optimal LRC codes for all lenghts n <= q
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abstract
A family of distance-optimal LRC codes from certain subcodes of $q$-ary Reed-Solomon codes, proposed by I.~Tamo and A.~Barg in 2014, assumes that the code length $n$ is a multiple of $r+1.$ By shortening codes from this family, we show that it is possible to lift this assumption, still obtaining distance-optimal codes.
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Optimal Quantum $(r,\delta)$-Locally Repairable Codes via Classical Ones
Optimal (r,δ)-locally repairable codes decompose into MDS local codes, forcing d≥δ, and this structure yields new optimal quantum (r,δ)-LRCs.