Geodesic
A criterion of perfect balance for shift-composition of functions over a finite alphabet
Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 59-65.

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We prove a criterion of perfect balance for sliding superposition of functions over an arbitrary finite alphabet. We also give examples of applying this result to the construction of perfectly balanced functions that are not permutations with respect to the first and to the last variable.
Keywords: functions over a finite alphabet, sliding superposition, perfectly balanced function, function with zero defect, permutability of a function with respect to a variable. 
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O. A. Logachev. A criterion of perfect balance for shift-composition of functions over a finite alphabet. Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 59-65. http://geodesic.mathdoc.fr/item/DM_2017_29_4_a3/

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