Cyclic Codes with Locality and Availability
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In this work the cyclic locally repairable code (LRC) construction by Tamo et al. is extended to (r,ρ)-locality and availability. We construct codes with a certain minimum distance by carefully extending the defining set of the code. We give a bound on the dimension of LRCs with availability and orthogonal repair sets and show that the given construction is optimal for a range of parameters.
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