Combinatorial Geometry and Coding Theory^*

Issue title: Discrete Mathematics (RuFiDiM 14)

Guest editors: J. Karhumäki, V. Mazalov and Yu. Matiyasevich

Article type: Research Article

Authors: Raigorodskii, A.M.^{a; b}

Affiliations: [a] Moscow Institute of Physics and Technology, State University, Dolgoprudny, Moscow, Russia | [b] Lomonosov Moscow State University, Moscow, Russia. mraigor@yandex.ru

Note: [*] This work is done under the financial support of the following grants: the grant 15-01-00350 of Russian Foundation for Basic Research, the grant NSh-2964.2014.1 supporting Leading scientific schools of Russia.

Abstract: In this paper, we overview three closely related problems: Nelson–Hadwiger problem on coloring spaces with forbidden monochromatics distances; Borsuk’s problem on partitioning sets in spaces into parts of smaller diameter; problem of finding codes with forbidden Hamming distances.

DOI: 10.3233/FI-2016-1365

Journal: Fundamenta Informaticae, vol. 145, no. 3, pp. 359-369, 2016