Three Efficient All-Erasure Decoding Methods for Blaum–Roth Codes

Blaum–Roth Codes are binary maximum distance separable (MDS) array codes over the binary quotient ring F2[x]/(Mp(x)), where Mp(x)=1+x+⋯+xp−1, and p is a prime number. Two existing all-erasure decoding methods for Blaum–Roth codes are the syndrome-based decoding method and the interpolation-based decoding method. In this paper, we propose a modified syndrome-based decoding method and a modified interpolation-based decoding method that have lower decoding complexity than the syndrome-based decoding method and the interpolation-based decoding method, respectively. Moreover, we present a fast decoding method for Blaum–Roth codes based on the LU decomposition of the Vandermonde matrix that has a lower decoding complexity than the two modified decoding methods for most of the parameters.