Codes for Distributed Storage: Recent Results
summary
Two concrete results: a high‑rate MSR construction that achieves rate = (T-1)/T with n = T·Q, k = (T-1)Q, d = n−1 and sub‑packetization alpha = Q^T, beta = Q^{T−1}, reducing exponential packetization to R^{n/R}-style growth by using linear array codes with jump parity checks (zigzag-style) and careful coefficient choices; field size needs at least n choose k to ensure data collection. Second, a hierarchical locality framework inserts middle local codes, proves tightened Singleton-like bounds, and generalizes Tamo–Barg and pyramid constructions via cyclic subgroup/coset indexing and precoding to raise global distance.
AI-written summary · about