An Optimal Result for Codes Identifying Sets of Words



: Janson S, Laihonen T

: 2009

: 2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1- 4

: 2547

: 2551

: 2

: 978-1-4244-4312-3

DOI: https://doi.org/10.1109/ISIT.2009.5206019


where r = pn, rho is an element of [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 is an element of [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 = [n/2] - 1.



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