This paper studies the design and secrecy performance of linear multihop networks, in the presence of randomly distributed eavesdroppers in a large-scale two-dimensional space. Depending on whether there is feedback from the receiver to the transmitter, we study two transmission schemes: on-off transmission (OFT) and non-on-off transmission (NOFT). In the OFT scheme, transmission is suspended if the instantaneous received signal-to-noise ratio (SNR) falls below a given threshold, whereas there is no suspension of transmission in the NOFT scheme. We investigate the optimal design of the linear multiple network in terms of the optimal rate parameters of the wiretap code as well as the optimal number of hops. These design parameters are highly interrelated since more hops reduces the distance of per-hop communication which completely changes the optimal design of the wiretap coding rates. Despite the analytical difficulty, we are able to characterize the optimal designs and the resulting secure transmission throughput in mathematically tractable forms in the high SNR regime. Our numerical results demonstrate that our analytical results obtained in the high SNR regime are accurate at practical SNR values. Hence, these results provide useful guidelines for designing linear multihop networks with targeted physical layer security performance.