On Generating the N-ary Reflected Gray Codes

Authors:
M. C. Er
Affiliations:
Department of Computing Science, University of Wollongong, Wollongong, Australia.
Venue:
IEEE Transactions on Computers
Year:
1984

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Abstract

The definition of the N-ary reflected Gray code is given. Two recursive algorithms for generating the N-ary reflected Gray codes are presented: one algorithm is coded directly from the definition; another algorithm is derived from the sequencing orders of digits in the N-ary reflected Gray codes. It is shown that these two algorithms are equivalent functionally. Furthermore, it is proven that the N-ary reflected Gray code is cyclic when its radix is even, but not cyclic, in general, when its radix is odd.