General Quadratic Prime Codes
广义平方素数码

Based on the relationship between the extension Galois fields and the prime Galois fields, this paper presents a new construction of frequency-hopping sequences, here designated as general quadratic prime codes, by expanding the construct idea of prime codes to extension Galois fields. Taking a general quadratic irreducible polynomial as the module and based on the multiplication of extension Galois fields, quadratic prime codes with more sequences and longer period possess ideal Hamming autocorrelation and nearly ideal Hamming cross-correlation properties of no greater than two. Furthermore, general quadratic prime codes can be further partitioned to get frequency hopping sequences groups in which the maximum Hamming cross-correlation between any two FH sequences in the same group is at most one.