A Note on Iterating an $\alpha$-ary Gray Code
Chi-Jen Lu, Shi‐Chun Tsai · SIAM Journal on Discrete Mathematics · 2001
In this note we consider the number of distinct $\alpha$-ary codes produced by repeatedly applying the Gray code mapping of Sharma and Khanna [ Inform. Sci., 15 (1978), pp. 31--43]. This number was derived before by Lichtner [SIAM J. Discrete Math., 11 (1998), pp. 381--386], and we give an alternative proof here. Our key observation is a simple connection between this number and the period of binomial coefficients modulo $\alpha$. Then the result follows immediately from a known periodic property of binomial coefficients modulo $\alpha$ [ Fibonacci Quart., 27 (1989), pp. 64--79; SIAM J. Discrete Math., 9 (1996), pp. 55--62; Ann. Univ. Mariae Curie-Sklodowska Sect. A, 10 (1956), pp. 37--47].