Repairing Reed-Solomon Codes via Subspace Polynomials
Son Hoang Dau, Thi Xinh Dinh, Han Mao Kiah, Trần Thị Lượng, Olgica Milenković · IEEE Transactions on Information Theory · 2021
We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature that employ trace polynomials. The Reed-Solomon codes are over \mathbb Fqland have redundancy r = n-k ≥ qm, 1 ≤ m ≤l, where n and k are the code length and dimension, respectively. In particular, for one erasure, we show that our schemes can achieve optimal repair bandwidths whenever n=qland r = qm, for all 1 ≤ m ≤l. For two erasures, our schemes use the same bandwidth per erasure as the single erasure schemes, forl/m is a power of q, and forl= qa, m=qb-1 > 1 ( a ≥ b ≥ 1), and for m ≥l/2 whenlis even and q is a power of two.