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On distance Gray codes

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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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Authors and Affiliations

  1. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    I. S. Bykov & A. L. Perezhogin

  2. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. L. Perezhogin

Authors
  1. I. S. Bykov
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  2. A. L. Perezhogin
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Correspondence to I. S. Bykov.

Additional information

Original Russian Text © I.S. Bykov, A.L. Perezhogin, 2017, published in Diskretnyi Analiz i Issledovanie Operatsii, 2017, Vol. 24, No. 2, pp. 5–17.

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Bykov, I.S., Perezhogin, A.L. On distance Gray codes. J. Appl. Ind. Math. 11, 185–192 (2017). https://doi.org/10.1134/S1990478917020041

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  • DOI: https://doi.org/10.1134/S1990478917020041

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