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Index system and separability of constant weight Gray codes

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1 Author(s)
van Zanten, A.J. ; Dept. of Math. & Inf., Delft Univ. of Technol., Netherlands

A number system is developed for the conversion of natural numbers to the codewords of the Gray code G(n,k) of length n and weight k, and vice versa. The focus is on the subcode G(n,k) of G(n) consisting of those words of G(n) with precisely k 1-bits, 0<k<n. This code is called the constant weight Gray code of length n and weight k. As an application sharp lower and upper bounds are derived for the value of |i-j|, where i and j are indices of codewords gi and gj of G(n,k) such that they differ in precisely 2 m bits

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 4 )