equations become: Using Gaussian elimination: Recalculate where to correct resulting in the corrected codeword: Gao decoder In 2002, an improved decoder was developed by Shuhong Gao, based on the extended Euclid algorithm. Example Using the same data as the Berlekamp Welch example above: Lagrange interpolation of for i = 1 to n divide Q(x) and E(x) by most significant coefficient of E(x) = 708. (Optional) Recalculate where to correct resulting in the corrected codeword: See also BCH code Cyclic code Chien search Berlekamp–Massey algorithm Forward error correction Berlekamp–Welch algorithm Folded Reed–Solomon code Notes References Further reading External links Information and tutorials Introduction to Reed–Solomon codes: principles, architecture and implementation (CMU) A Tutorial on Reed–Solomon Coding for Fault-Tolerance in RAID-like Systems Algebraic soft-decoding of Reed–Solomon codes Wikiversity:Reed–Solomon codes for coders BBC R&D White Paper WHP031 Concatenated codes by Dr. Dave Forney (scholarpedia.org). Implementations FEC library in C by Phil Karn (aka KA9Q) includes Reed–Solomon codec, both arbitrary and optimized (223,255) version Schifra Open Source C++ Reed–Solomon Codec Henry Minsky's RSCode library, Reed–Solomon encoder/decoder Open Source C++ Reed–Solomon Soft Decoding library Matlab implementation of errors and-erasures Reed–Solomon decoding Octave implementation in communications package Pure-Python implementation of a Reed–Solomon codec Error detection and correction Coding theory