We present a deterministic operator on tree codes -- we call tree code product -- that allows one to deterministically combine two tree codes into a larger tree code. Moreover, if the original tree codes are efficiently encodable and decodable, then so is their product. This allows us to give the first deterministic subexponential-time construction of explicit tree codes: we are able to construct a tree code T of size n in time 2^{n^epsilon}. Moreover, T is also encodable and decodable in time 2^{n^epsilon}.

We then apply our new construction to obtain a deterministic constant-rate error-correcting scheme for interactive computation over a noisy channel. If the length of the interactive computation is n, the amount of computation required is deterministically bounded by n^{1+o(1)}, and the probability of failure is n^{-\omega(1)}.