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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 wordrto be decoded, are constructed and compared withr. An operationally simple algorithm of this type is studied for cyclic code spacesA. LetAhave lengthn, dimensionkover some finite field, and minimal Hamming distancem. The construction of fewer thann^2/2code words is required in decoding a wordr. The procedure seems to be most efficient for small minimal distancem, but somewhat paradoxically it is suggested on operational grounds that it may prove most useful in those cases wheremis relatively large with respect to the code lengthn.

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