The maximum number of edges spanned by a subset of given diameter in a Hamming space with alphabet size at least three is determined. The binary case was solved earlier by Ahlswede and Khachatrian [A diametric theorem for edges, J. Combin. Theory Ser. A 92(1) (2000) 1–16]. © 2007 Elsevier B.V. All rights reserved.

background: the study was developed in order to find a subset of potential factors, which affect birth distance pattern, regarding consideration on correlation of events of birth in a family and correlation within clusters/centers which other studies omit these correlations. methods: referring to documents that were registered for family in the health care centers on socio-economical zone, we c...

The COVID-19 pandemic has fundamentally affected all the spheres of human life, including education. Universities worldwide have established distance learning, which demanded combining and improving both traditional innovative education forms. article offers a comprehensive analysis pre-recorded mini-lectures in educational space learningfor different scientific-educational Internet projects (C...

The number of potential applications has made automatic recognition of human actions a very active research area. Different approaches have been followed based on trajectories through some state space. In this paper we also model an action as a trajectory through a state space, but we represent the actions as a sequence of temporal isolated instances, denoted primitives. These primitives are ea...

In this paper, we present some new results on the thinnest coverings that can be obtained in Hamming or Euclidean spaces if spheres and ellipsoids are covered with balls of some radius ε. In particular, we tighten the bounds currently known for the ε-entropy of Hamming spheres of an arbitrary radius r. New bounds for the ε-entropy of Hamming balls are also derived. If both parameters ε and r ar...

In this paper, we present some new results on the thinnest coverings that can be obtained in Hamming or Euclidean spaces if spheres and ellipsoids are covered with balls of some radius ε. In particular, we tighten the bounds currently known for the ε-entropy of Hamming spheres of an arbitrary radius r. New bounds for the ε-entropy of Hamming balls are also derived. If both parameters ε and r ar...