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 F-2[X]/(M-p(x)), where M-p(x) = 1 + x + ... + x(P-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.

Automated summary

This paper introduces two existing decoding methods and three modified decoding methods for Blaum-Roth codes, which have lower decoding complexity than the existing ones.