On binary linear <Emphasis Type="Italic">r</Emphasis>-identifying codes

A subspace C of the binary Hamming space F ⁿ of length n is called a linear r-identifying code if for all vectors of F ⁿ the intersections of C and closed r-radius neighbourhoods are nonempty and different. In this paper, we give lower bounds for such linear codes. For radius r =  2, we give some general constructions. We give many (optimal) constructions which were found by a computer search. New constructions improve some previously known upper bounds for r-identifying codes in the case where linearity is not assumed.