An efficient interpolation-based systematic encoder for low-rate Blaum-Roth codes

In this paper, we propose an efficient interpolation-based systematic encoder for low-rate Blaum-Roth codes. Our algorithm is based upon an equivalent definition of [p, k] Blaum-Roth codes from the perspective of generator matrices. Moreover, applying the interpolation method first proposed by D.J.J. Versfeld et al. to the generator matrix, we then derive a formula to resolve the erasure-only decoding problem. Finally, we present a straightforward systematic encoder based on this formula. Compared to the encoders in [5] and [14], it is more efficient for low-rate codes.