Finite Heisenberg-Weyl groups and golay complementary sequences

We provide a new way of understanding Golay pairs (of length N) of sequences in terms of the (2N + 1)-dimensional discrete Heisenberg-Weyl group over the field Z₂. Our methodology provides a different insight into the nature of these sequences, as well as a mechanism for designing sequences with desirable correlation properties. Libraries of waveforms formed using these constructions are able to provide collections of ambiguity functions that cover the range-Doppler plane in an efficient way, and thus provide the basis for a suite of waveforms optimized for extraction of information from the environment in an active sensing context.