Derives the incidence-multiplicity lower bound ℓ(n-1) - (r-1)(q^ℓ-1)/(q-1) on repair bandwidth and I/O for MDS array codes with r≥2 and shows it is attained by field reductions of normal rational curves for specified parameters.
[RRT25] Vinayak Ramkumar, Netanel Raviv, and Itzhak Tamo
2 Pith papers cite this work. Polarity classification is still indexing.
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A projective counting lower bound on linear exact repair costs for MDS array codes is attained for r=2 using Desarguesian spreads.
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The Incidence-Multiplicity Bound for Linear Exact Repair in MDS Array Codes
Derives the incidence-multiplicity lower bound ℓ(n-1) - (r-1)(q^ℓ-1)/(q-1) on repair bandwidth and I/O for MDS array codes with r≥2 and shows it is attained by field reductions of normal rational curves for specified parameters.
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Linear Exact Repair in MDS Array Codes: A General Lower Bound and Its Attainability
A projective counting lower bound on linear exact repair costs for MDS array codes is attained for r=2 using Desarguesian spreads.