  Random linear network code has to sacrifice part of bandwidth to transfer the
coding vectors, thus a head of size k log|T| is appended to each packet. We
present a distributed random network coding approach based on the Chinese
remainder theorem for general multicast networks. It uses a couple of modulus
as the head, thus reduces the size of head to O(log k). This makes it more
suitable for scenarios where the number of source nodes is large and the
bandwidth is limited. We estimate the multicast rate and show it is
satisfactory in performance for randomly designed networks.
