For digital underwater transmission an information sequence (17) of digital bits is partitioned into a succession of symbols each comprising n bits where n is equal to or greater than one (2ⁿ potential symbols), each symbol (19) is replaced (20) a corresponding base code sequence of length m bits and the result (21) is passed to an acoustic transducer after bi-phase modulation (22) on a carrier. The code has good correlation properties, e.g. a pseudo-random maixmal length sequence, a Gold code or a Kasami code, and the value of m/n is at least (32). Preferably the base sequence is cyclically extended at one or both ends prior to modulation, and Solomon Reed redundancy coding (18) is initially applied to the information sequence. The output (23) of modulator (22) may be prefaced (26) by a pair of chirp waveforms (24). Provision is made for Doppler and multi-path correction.