New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case

Abstract—New designs for families of sequences over GF () with low cross correlation, balance property, and large linear span are presented. The key idea of the new designs is to use short-ary sequences of period with the two-level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties. The resulting sequences are interleaved sequences of period 2. There are cyclically shift dis-tinct sequences in each family. The maximal correlation value is 2 +3 which is optimal with respect to the Welch bound. Each se-quence in the family is balanced and has large linear span. In par-ticular, for binary case, cross/out-of-phase autocorrelation values belong to the set 1 + 2 2 + 3 2 1, any se-quence where the short sequences are quadratic residue sequences achieves the maximal linear span. It is shown that some families of these sequences can be implemented efficiently in both hardwar