Improved Upper Bounds on Binary Identifying Codes
Geoffrey Exoo, Tero K Laihonen, Sanna Ranto · IEEE Transactions on Information Theory · 2007
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$1$-identifying codes of many lengths when$n\geq 10$. We construct$t$-identifying codes using the direct sum of$t$$1$-identifying codes. This solves partly an open problem posed by Blass, Honkala, and Litsyn in 2001. We also prove a general result concerning the direct sum of a$t$-identifying code with the whole space of any dimension.