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Optimal LRC codes for all lenghts n <= q

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arxiv 1802.00157 v1 pith:XCNPPL5D submitted 2018-02-01 cs.IT math.IT

Oleg Kolosov , Alexander Barg , Itzhak Tamo , Gala Yadgar This is my paper · ORCID
classification cs.ITmath.IT
keywords codesdistance-optimalfamilyassumesassumptionbargcertaincode
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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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  1. Optimal Quantum $(r,\delta)$-Locally Repairable Codes via Classical Ones

    quant-ph 2025-07 conditional novelty 7.0 of 10

    Optimal (r,δ)-locally repairable codes decompose into MDS local codes, forcing d≥δ, and this structure yields new optimal quantum (r,δ)-LRCs.

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