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 r to be decoded, are constructed and compared with r . An operationally simple algorithm of this type is st...

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Bibliographic Details
Published inI.R.E. transactions on information theory Vol. 8; no. 5; pp. 5 - 9
Main Author Prange, E.
Format Journal Article
LanguageEnglish
Published The Institute of Radio Engineers, Inc 01.09.1962
Subjects
Classification algorithms
Concrete
Decoding
Equations
Galois fields
Hamming distance
Hamming weight
Laboratories
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ISSN0096-1000
DOI10.1109/TIT.1962.1057777

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Summary: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 .
ISSN:0096-1000
DOI:10.1109/TIT.1962.1057777