Syndrome-coding for the wiretap channel revisited

To communicate an r-bit secret s through a wire-tap channel, the syndrome coding strategy consists of choosing a linear transformation h and transmitting an n-bit vector x such that h(x) = s. The receiver obtains a corrupted version of x and the eavesdropper an even more corrupted version of x: the (syndrome) function h should be chosen in such a way as to minimize both the length n of the transmitted vector and the information leakage to the eavesdropper. We give a refined analysis of the information leakage that involves m-th moment methods