Quadratic prime codes

This letter presents a new construction of frequency-hopping (FH) sequences, here designated as quadratic prime codes by expanding the construct idea of prime codes to the extension Galois fields GF(P²). Taking f(x)=x²−y as the irreducible polynomial, where is a quadratic nonresidue of prime number P, quadratic prime codes of length P² are generated, which possess ideal Hamming autocorrelation and nearly ideal Hamming cross-correlation properties. Furthermore, quadratic prime codes can be partitioned into P+1 groups, of which the maximum Hamming cross-correlation between any two FH sequences in the same group is at most one.