Two families of four-phase sequences are constructed using irreducible polynomials over Z/sub 4/. Family A has period L=2/sup r/-1. size L+2. and maximum nontrivial correlation magnitude C/sub max/>or=1+ square root (L+1), where r is a positive integer. Family B has period L=2(2/sup r/-1). size (L+2)/4. and C/sub 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 square root 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.
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机译：使用Z / sub 4 /上的不可约多项式构造两个四相序列族。家庭A的周期L = 2 / sup r / -1。尺寸L + 2。最大非平凡相关幅度C / sub max />或= 1 +平方根（L + 1），其中r是一个正整数。家庭B的周期L = 2（2 / sup r / -1）。大小（L + 2）/ 4。和C / sub max /用于复数值序列。特别令人感兴趣的是，家族A具有与二进制Gold序列家族相同的大小和周期。但其最大非平凡相关性却减小了平方根2倍。由于r奇数的Gold族相对于限于二进制序列的Welch界是最优的，因此A族优于同一个族的最佳可能二元设计尺寸。与Gold设计不同，无论r是奇数还是偶数，A和B族都是渐近最优的。这两个系列均适合于实现码分多址，并且很容易使用移位寄存器来实现。给出了两个家族的相关值的精确分布。
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