The use of information sets in decoding cyclic codes - Prange, E. (I.R.E. transactions on information theory, 1962)
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 r to be decoded, are constructed and compared with r . An operationally simple algorithm of this type is studied for cyclic code spaces A . Let A have length n , dimension k over some finite field, and minimal Hamming distance m . The construction of fewer than n^2/2 code words is required in decoding a word r . The procedure seems to be most efficient for small minimal distance m , but somewhat paradoxically it is suggested on operational grounds that it may prove most useful in those cases where m is relatively large with respect to the code length n .