4-phase sequences with near-optimum correlation properties

Two families of four-phase sequences are constructed using irreducible polynomials over Z₄. Family A has period L =2^r-1. size L+2. and maximum nontrivial correlation magnitude C_max⩽1+√(L+1), where r is a positive integer. Family B has period L=2(2^r-1). size (L+2)/4. and C_max for complex-valued sequences. Of particular interest, family A has the same size and period as the family of binary Gold sequences. but its maximum nontrivial correlation is smaller by a factor of √2. Since the Gold family for r odd is optimal with respect to the Welch bound restricted to binary sequences, family A is thus superior to the best possible binary design of the same family size. Unlike the Gold design, families A and B are asymptotically optimal whether r is odd or even. Both families are suitable for achieving code-division multiple-access and are easily, implemented using shift registers. The exact distribution of correlation values is given for both families