Geodesic
On the weak isometries of the Boolean cube
Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 4, pp. 26-32.

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The $p$-weak isometries of the Boolean cube are considered, i.e., the mappings of the cube onto itself which preserve a fixed distance $p$. Some necessary and sufficient conditions are obtained for coincidence of the group of $p$-weak isometries with the group of standard isometries (automorphisms of the cube). 
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V. Yu. Krasin. On the weak isometries of the Boolean cube. Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 4, pp. 26-32. http://geodesic.mathdoc.fr/item/DA_2006_13_4_a2/

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[2] Beckman F. S., Quarles D. A., “On isometries of Euclidean spaces”, Proc. of the American Math. Soc., 4, no. 5, 1953, 810–815 | MR | Zbl