Expander Graphs are Non-Malleable Codes

Any $d$-regular graph on $n$ vertices with spectral expansion $\lambda$ satisfying $n=\mathrm{\Omega }(d^3\log (d)\mathrm{/}\lambda )$ yields a $O\left(\frac{{\lambda }^{3\mathrm{/}2}}{d}\right)$-non-malleable code for single-bit messages in the split-state model.