Hamming, Golay and Reed-Muller Codes.

The article discusses the linear binary codes, Hamming, Golay and Reed-Muller code. These codes are examples of error-correcting codes. Hamming codes are perhaps the most widely known class of block codes, with the possible exception of Reed-Solomon codes. Hamming codes require the smallest amount of redundancy, for a given block length, to correct any single error, so it provides a optimal coding scheme. The binary Golay code is the only other nontrivial example of an optimal triple-error correcting code. Reed-Muller codes can be defined as codes with an elegant combinatorial definition that are easy to decode.