Efficient Erasure Decoding for Generalized Reed Solomon Codes

We present an efficient erasure decoding algorithm for generalized Reed Solomon codes constructed by utilizing the structure of the inverse of the VanderMonde matrices. Given an [n, k] generalized Reed Solomon code, decoding for r erasures, where r = n − k, requires rk + n Galois field multiplications and r(k − 1) Galois field additions after setting up the decoding structures for an erasure pattern. Setting up the decoding structures requires r + r(k − 1) field multiplications, r(r − 1) + 2rk field additions, r + r(k + 1) field negations and r(k + 1) field inversions.