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Some properties of nonbinary error-correcting codes

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An error-correcting code may be thought of as a subsetS_0of points belonging to a setSin which a metric is defined such that the distance between every pair of distinct points ofS_0is larger than some given number. In Hamming's original formulation,Swas taken to be the set of all2^nn-bit binary numbers and the distance between a pair of binary numberssandtwas taken to be the number of bits ofswhich do not agree with the corresponding bits oft. In this note we shall takeSto be the set of alln-tuples in which each coordinate of ann-tuple can assume one ofkintegral values:0, 1, cdots, k - 1, withk geqq 2. Properties of these nonbinary codes will be discussed.

Published in:

Information Theory, IRE Transactions on  (Volume:4 ,  Issue: 2 )

Date of Publication:

June 1958

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