New families of q-ary optimal locally repairable codes with availability are built via ordinary elliptic function fields, giving length O(q+2√q) and a q²-ary family with two recovering sets of length O(q²+2q) and small Singleton defect.
On the locality of codeword symbols
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Derives information-theoretic lower bounds on conversion bandwidth for systematic optimal-distance LRC convertible codes in the global merge regime, proving optimality of Maturana-Rashmi constructions without linearity assumptions.
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Locally Repairable Codes with Availability via Elliptic Function Fields
New families of q-ary optimal locally repairable codes with availability are built via ordinary elliptic function fields, giving length O(q+2√q) and a q²-ary family with two recovering sets of length O(q²+2q) and small Singleton defect.
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Bandwidth Cost of Locally Repairable Convertible Codes in the Global Merge Regime
Derives information-theoretic lower bounds on conversion bandwidth for systematic optimal-distance LRC convertible codes in the global merge regime, proving optimality of Maturana-Rashmi constructions without linearity assumptions.