The use of information sets in decoding cyclic codes

A class of decoding algorithms using encoding-and-comparison is considered for error-correcting code spaces. Code words, each of which agrees on some information set for the code with the word to be decoded, are constructed and compared with . An operationally simple algorithm of this type is studied for cyclic code spaces . Let have length , dimension over some finite field, and minimal Hamming distance . The construction of fewer than code words is required in decoding a word . The procedure seems to be most efficient for small minimal distance , but somewhat paradoxically it is suggested on operational grounds that it may prove most useful in those cases where is relatively large with respect to the code length .