On distance Gray codes |
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Authors: | I S Bykov A L Perezhogin |
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Institution: | 1.Novosibirsk State University,Novosibirsk,Russia;2.Sobolev Institute of Mathematics,Novosibirsk,Russia |
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Abstract: | A Gray code of size n is a cyclic sequence of all binary words of length n such that two consecutive words differ exactly in one position. We say that the Gray code is a distance code if the Hamming distance between words located at distance k from each other is equal to d. The distance property generalizes the familiar concepts of a locally balanced Gray code. We prove that there are no distance Gray codes with d = 1 for k > 1. Some examples of constructing distance Gray codes are given. For one infinite series of parameters, it is proved that there are no distance Gray codes. |
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