Geodesic
Hausdorff metric on faces of the $n$-cube
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 151-155

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The Hausdorff metric on all faces of the unit $n$-cube ($\mathrm I^n$) is considered. The notion of a cubant is used; it was introduced as an $n$-digit quaternary code of a $k$-dimensional face containing the Cartesian product of $k$ frame unit segments and the face translation code within $\mathrm I^n$. The cubants form a semigroup with a unit (monoid) with respect to the given operation of multiplication. A calculation of Hausdorff metric based on the generalization of the Hamming metric for binary codes is considered. The supercomputing issues are discussed. 
@article{FPM_2010_16_1_a11,
     author = {G. G. Ryabov},
     title = {Hausdorff metric on faces of the $n$-cube},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {151--155},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a11/}
}
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G. G. Ryabov. Hausdorff metric on faces of the $n$-cube. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 151-155. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a11/