Permutation decoding the binary images of certain double-parity reed-solomon codes

We introduce two permutation decoder designs for the binary images of double-parity [n, n − 2, 3] Reed-Solomon (RS) codes over binary extension fields F2m. The codes considered are limited to have zeros {1, α}, where α is any primitive element in F2m. We show that there exists a large set of m binary symbol errors that may be corrected via permutation decoding. The permutation decoders are shown to achieve near maximum-likelihood decoder performance, while only utilizing simple ideas borrowed from well-known reliability-based decoding algorithms.