A1 Refereed original research article in a scientific journal
On the size of identifying codes in binary hypercubes
Authors: Janson S, Laihonen T
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2009
Journal: Journal of Combinatorial Theory, Series A
Journal name in source: JOURNAL OF COMBINATORIAL THEORY SERIES A
Journal acronym: J COMB THEORY A
Volume: 116
Issue: 5
First page : 1087
Last page: 1096
Number of pages: 10
ISSN: 0097-3165
DOI: https://doi.org/10.1016/j.jcta.2009.02.004
Abstract
where r = left perpendicular rho nright perpendicular, rho epsilon [0, 1) and h(x) is the binary entropy function. In this paper, we prove that this result holds for any fixed l >= 1 when rho epsilon [0, 1/2). We also show that M(r)((<= l))(n) = O(n(3/2)) for every fixed l and r slightly less than n/2, and give an explicit construction of small (r, <= 2)-identifying codes for r = left perpendicularn/2right perpendicular - 1. (C) 2009 Elsevier Inc. All rights reserved.
where r = left perpendicular rho nright perpendicular, rho epsilon [0, 1) and h(x) is the binary entropy function. In this paper, we prove that this result holds for any fixed l >= 1 when rho epsilon [0, 1/2). We also show that M(r)((<= l))(n) = O(n(3/2)) for every fixed l and r slightly less than n/2, and give an explicit construction of small (r, <= 2)-identifying codes for r = left perpendicularn/2right perpendicular - 1. (C) 2009 Elsevier Inc. All rights reserved.
UTU Research Portal