Bit-level erasure decoding of Reed-Solomon codes over GF(2m)

The algorithms for bit-level erasure decoding of (n,k) Reed-Solomon codes over GF(2^m) beyond the design erasure decoding distance of n-k are considered. Erasure decoding takes place in the (mk, nk) binary image code. When the number of erasures exceeds n-k, then additional parity check equations must be developed. We describe how these equations are obtained and some of their properties. Decoding algorithms are discussed which tradeoff decoding performance for computational complexity. Simulation results for several families of codes are presented which provide information about good binary image codes.