Performance Analysis of Quadratic Prime Codes and Construction of New Frequency-Hopping Sequences

Quadratic prime codes are new types of frequency-hopping (FH) sequences constructed by expanding the construct idea of prime codes to finite extension fields. The linear complexity and characteristics of frequency interval of quadratic prime codes are analyzed and compared with those of prime codes. The results show that, on one hand, the linear complexity of quadratic prime codes is about half the length of the sequences, and therefore has ideal characteristics of linear complexity, while the linear complexity of prime codes is always 2. The linear complexity of quadratic prime codes is much greater than that of prime codes, and thus quadratic prime codes have better confidentiality. On the other hand, quadratic prime codes do not have characteristics of wide frequency interval while prime codes have excellent characteristics of wide frequency interval. Furthermore, two methods for constructing FH sequences with wide frequency interval are proposed based on the combination of prime codes and quadratic prime codes. The Hamming correlation and linear complexity of the proposed FH sequences are derived theoretically and computed explicitly. Results show that the proposed FH sequences have the advantage of prime codes and quadratic prime codes, e.g., they not only have wide frequency interval and uniform frequency, but also have good Hamming correlation and ideal linear complexity.