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The use of information sets in decoding cyclic codes

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1 Author(s)

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 .

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Information Theory, IRE Transactions on  (Volume:8 ,  Issue: 5 )