We describe a new architecture for laser displacement metrology with a drastic reduction in the size and complexity of the optical head. Connected by a single optical fiber, the compact heads are easy to integrate and readily multiplexed to support applications requiring large numbers of sensors. The approach is made possible by modulating the outgoing laser light with a binary random noise code, allowing the detected signals to be discriminated based on their propagation delay. We demonstrate a displacement resolution of 1.1 nm rms.