26 April 2006 On the construction of generalized Gray code
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Proceedings Volume 6159, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments IV; 61594G (2006) https://doi.org/10.1117/12.674968
Event: Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments IV, 2005, Wilga, Poland
Abstract
This paper concerns the problem of expanding the standard classical Gray code [l]. The incentive reason which stipulates interest to Gray transformations is to find the base Walsh systems that provide much faster operating speed to the fast Fourier transform (FFT) processors on comparison with the base discrete exponential functions (DEF). This result is useful to find more effective method for estimation of Doppler frequency in discovery - measuring of wideband radio-location signals in frequency space. The generalized Gray code is constructed by various methods. At first, the expansion of Gray codes can be attained due to increasing the number of channels, by which the entrance operands of transformation are related to the output operands. And, secondly, in the separate (all) flow lines of operands(graph's ribs of transformation) we can insert additional multiplying elements with the coefficient of transmission, which is the positive integer and the module does not exceed m-1. In the paper, the algorithms of transformation of digital code combinations are offered, dilative the number of simple Gray transformation. By the achieved generalized Gray codes the problem of clusterization is successfully resolved. This problem can be described that: by only simple original Gray codes not for all parameters of m (base number) and n (bit's number of code) is succeeded link all elements in great symmetric systems of the Vilenkina-Chrestenson functions. Useful applications of the generalized Gray transformations can turn out in cryptography, antinoise coding and others.
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Anatoly Beletsky, Nguyen Viet Hung, "On the construction of generalized Gray code", Proc. SPIE 6159, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments IV, 61594G (26 April 2006); doi: 10.1117/12.674968; https://doi.org/10.1117/12.674968
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