Geodesic
The Shannon function for calculating the Arnold complexity of length $2^n$ binary words for arbitrary $n$
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 59-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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The exact value of the Shannon function for fast calculating the Arnold complexity of length $2^n$ binary words is obtained for $n=m^2$, $n=m^2+m$, and $n=m^2+2m$, $m\geq2$. Thus the exact value of the Shannon function is determined for an arbitrary $n$. Bibliogr. 6.
Keywords: binary word, complexity of word, Arnold complexity, Shannon function. 
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Yu. V. Merekin. The Shannon function for calculating the Arnold complexity of length $2^n$ binary words for arbitrary $n$. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 59-75. http://geodesic.mathdoc.fr/item/DA_2014_21_2_a4/

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[6] Merekin Yu. V., “Fast computation of the Arnold complexity of length $2^n$ binary words”, Southeast Asian Bull. Math., 36:6 (2012), 855–862 | MR | Zbl