A class of frequency hop codes using only three frequencies

Costas (1984) and sonar sequences are those patterns for which you send out exactly one signal at every time slot, and with the special property that even if only two signals return you can reconstruct the whole pattern. This last point means that there is no ambiguity. This is also referred in the literature as having perfect or one hit auto-correlation. The goal involved in constructing sonars is, given n to obtain an n by l sequence for l as large as possible. Different from the Costas or sonar sequences the auto-correlation function of our pattern is not perfect and actually the numbers of hits grows with larger lengths. On the other hand the number of frequencies is always fixed to 3 and is therefore easy and cost effective to implement. We compare our construction with the table of Maric and Titlebaum (1992) best sonars and our new construction compares quite favorably with the table of best sonars of Moreno, Games and Taylor (1993).