In vehicular ad hoc networks (VANETs), for a large number of applications, the destination of relevant information such as alerts, is the whole set of vehicles located inside a given area. Therefore dissemination with efficient broadcast is an essential communication primitive. One of the families of broadcast protocols suitable for such networks, is the family of delay-based broadcast protocols, where farthest receivers retransmit first and where transmissions also act as implicit acknowledgements. For lossless networks, such protocols may approach the optimum efficiency. However with realistic loss models of VANET wireless communication, their performance is noticeably degraded. This is because packet losses have a double effect: directly on the amount of successfully received packets and indirectly with implicit acknowledgement misses. In this article, in order to combat the effects of packet losses, we combine delay-based broadcast with network coding, through a new protocol: Delay-based Opportunistic Network Coding protocol (DONC). By design, DONC aims at cancelling the twofold effects of packet and implicit acknowledgement losses. We describe the details of the DONC protocol, and we study its behavior, with realistic models and simulations. Results illustrate the excellent performance of the protocol.