Improved upper bounds on binary identifying codes

In binary Hamming spaces, we construct new 1-identifying codes from 2-fold 1-coverings that are 1-identifying. We improve on previously known upper bounds for the cardinalities of I-identifying codes of many lengths when n >= 10. We construct t-identifying codes using the direct sum of t I-identifying codes. This solves partly an open problem posed by Blass, Honkala, and Litsyn in 2001. We also prove a general result concerning the direct sum of a t-identifying code with the whole space of any dimension.