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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 subset S_0 of points belonging to a set S in which a metric is defined such that the distance between every pair of distinct points of S_0 is larger than some given number. In Hamming's original formulation, S was taken to be the set of all 2^n n -bit binary numbers and the distance between a pair of binary numbers s and t was taken to be the number of bits of s which do not agree with the corresponding bits of t . In this note we shall take S to be the set of all n -tuples in which each coordinate of an n -tuple can assume one of k integral values: 0, 1, \cdots , k - 1 , with k \geq q 2 . Properties of these nonbinary codes will be discussed.

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