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Packet loss in vehicular networks can undermine the effectiveness of communication-based accident prevention systems. Traditionally, retransmission has been used to combat packet loss in communication networks. However, retransmission overhead is known to increase channel congestion in dense wireless vehicular networks, which increases the likelihood of packet loss due to collisions, limiting the loss recovery capacity of the retransmission algorithm. This paper presents a low-overhead retransmission algorithm called blind xor (BXOR). By xoring multiple packets into a single retransmission, BXOR recovers an increased number of lost packets per retransmission. BXOR keeps the overhead low by not trying to learn the loss status of the receivers via feedback, rather, which packets to xor are blindly decided by the retransmitter alone. It is mathematically proved that BXOR can outperform existing retransmission methods if the conditional reception probability (CRP) of the xored packets is greater than 0.5. The performance is maximized by xoring an optimal number of packets, which is a function of the CRP. It is also proved that there is a negative performance if BXOR is exercised for a CRP of less than 0.5. Guided by the analytical results, we propose a practical BXOR protocol, which opportunistically exercises the xor operation based on the current estimation of the CRP. Simulation experiments confirm that, within a 110-m radius of the original packet transmitter, BXOR can reduce the packet reception failure rate by up to 60% of the rates achievable by previously proposed retransmission algorithms.