An Efficient Reed-Solomon Erasure Code over Cantor-constructed Binary Extension Finite Fields

In this paper, we investigate the properties of the novel polynomial basis proposed by Lin, Chung, and Han over Cantor-constructed binary extension finite fields and propose an improved truncated LCH transform for discrete intervals. Incorporating these results leads us to the development of efficient encoding/decoding algorithms of (n,k) Reed-Solomon erasure codes with time complexity O(nlog(T)) and O (1) space complexity, where T < n. We also propose its performance-tuned variation of the decoding algorithm when only recovery of message symbols is concerned. Our experiment in the production environment indicates a performance gain of ×1 on average and ×2 at most towards the original decoder algorithm.