Achieving Arbitrary Locality And Availability In Binary Codes
Wang Anyu, Zhang Zhifang. Arxiv 2015
The \(i\)th coordinate of an \((n,k)\) code is said to have locality \(r\) and availability \(t\) if there exist \(t\) disjoint groups, each containing at most \(r\) other coordinates that can together recover the value of the \(i\)th coordinate. This property is particularly useful for codes for distributed storage systems because it permits local repair and parallel accesses of hot data. In this paper, for any positive integers \(r\) and \(t\), we construct a binary linear code of length \(\binom{r+t}{t}\) which has locality \(r\) and availability \(t\) for all coordinates. The information rate of this code attains \(\frac{r}{r+t}\), which is always higher than that of the direct product code, the only known construction that can achieve arbitrary locality and availability.
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