The authors construct new and improved sonar sequences by applying rotation, multiplication, and shearing transformations to Costas sequence constructions. A catalog of the best known sonar sequences with up to 100 symbols is given.>

In pulse position modulation (PPM) communications an acquisition sequence is needed to establish frame synchronization for subsequent data transmission. This sequence must have PPM structure (one pulse per frame) and desirable autocorrelation properties for its detection. The problem of finding aperiodic PPM acquisition sequences having the minimum possible autocorrelation for all off-shifted positions is investigated. Sequences with the maximum possible number of frames have been found up to frame size15. Examples are given for every frame length up to88, and powers of two up to1024. An interesting relation between the PPM sequence problem, Costas and sonar arrays, and Golomb's ruler is explored.

A number of closely related combinatorial problems corresponding to specific assumptions about the type of time-frequency sequence which may be appropriate in a particular application, are formulated in terms of square or rectangular arrays of dots with appropriate constraints on the two-dimensional correlation function. The current state of knowledge concerning each of these problems is summarized. It is hoped that more general constructions may be found, leading to larger families of solutions, as well as better computational algorithms for finding individual solutions which may lie outside of the general families.