On systematic encoding for Blaum-Roth codes

We propose a new systematic encoding procedure for Blaum-Roth codes, i.e., Reed-Solomon(RS) codes over the polynomial rings modulo Σ_i=o^p-1xⁱ over GF(q), where p is a prime. Our method generalizes the interpolation-based erasure-only decoder for RS codes proposed by D.J.J. Versfeld et al., which is efficient for low-rate RS codes. Later, we derive a systematic encoder from this decoder, since encoding can be implemented as a special case of decoding. Compared to the systematic encoding procedure introduced by M. Blaum an R. Roth, our encoding procedure is very efficient for low-rate Blaum-Roth codes.