2603.00076 Non-Monotonicity of Optimal Identifying Code Size in Hypercubes (with Rigorous Certificates for r=2 and Explicit Counterexamples for r > n/2)
Identifying codes, introduced by Karpovsky–Chakrabarty–Levitin, are useful for fault localization in networks. In the binary Hamming space (hypercube) Q_n, let M_r(n) denote the minimum size of an r-identifying code.