New constructions of binary cyclic codes [2^m-1, 2^{m-1}±1, d] with d ≥ 2^{m/2}-1 and d^perp ≥ 2^{m/2} (m even), plus similar families for m odd and m product of two primes, achieving d·d^perp asymptotically 2n.
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Generalizes the Guruswami-Wooters repair scheme to GRM codes to achieve bandwidth close to the lower bound for single failures when the subfield is small, and extends the approach to multiple failures while computing expected bandwidth over erasure patterns.
citing papers explorer
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New Constructions of Binary Cyclic Codes with Both Relatively Large Minimum Distance and Dual Distance
New constructions of binary cyclic codes [2^m-1, 2^{m-1}±1, d] with d ≥ 2^{m/2}-1 and d^perp ≥ 2^{m/2} (m even), plus similar families for m odd and m product of two primes, achieving d·d^perp asymptotically 2n.
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Repairing Generalized Reed-Muller Codes
Generalizes the Guruswami-Wooters repair scheme to GRM codes to achieve bandwidth close to the lower bound for single failures when the subfield is small, and extends the approach to multiple failures while computing expected bandwidth over erasure patterns.