Based on the concept of linear congruence [1, 2], prime codes were traditionally designed to have low cross-correlation functions and support asynchronous transmissions. In 1978, Cooper and Nettleton [3] introduced the first version of prime codes for cellular mobile frequency-hopping spread-spectrum communication systems, supporting asynchronous transmissions from mobile units to a base station [4–7]. In 1981, Titlebaum [8] introduced a family of frequency-time prime codes for coherent multiuser radar and asynchronous frequency-hopping spread-spectrum communication systems. Belonging to a family of extended cyclic Reed–Solomon codes, these prime codes are maximum distance separable cyclic codes [1, 2]. In 1983, ...
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