Prime-phase sequences with periodic correlation properties better than binary sequences
Prime-phase sequences with periodic correlation properties better than binary sequences
复制标题
DOI：
10.1109/18.79916
复制
发表时间：
1991-05
期刊：
影响因子：
--
通讯作者：
Vijay Kumar;O. Moreno
中科院分区：
文献类型：
--
作者：
Vijay Kumar;O. Moreno
对于p是奇素数，n=2是整数，并且omega是复本原第p个单位根的情况，给出了p/sup n/p相序列(形式为omega/sup i/的符号)族的构造，其中每个序列具有长度p/sup n/-1，并且其中最大非平凡相关值C/submax/不超过1+平方根p/sup n/。提供了相关值的完整分布。作为这种构造的特例，得到了Sidelnikov(1971)以前的构造。该序列族在其相关性方面是渐近最优的，并且与许多以前的非二进制设计相比，本设计具有不需要大小大于3的字母表的附加优势。新序列适合于实现码分多址，并且很容易用移位寄存器实现。它们是通过Deligne界(1974)在多元Weil型指数和上的应用而发现的。序列对某些Bent函数也有很强的辨识性。>；
For the case where p is an odd prime, n>or=2 is an integer, and omega is a complex primitive pth root of unity, a construction is presented for a family of p/sup n/ p-phase sequences (symbols of the form omega /sup i/), where each sequence has length p/sup n/-1, and where the maximum nontrivial correlation value C/sub max/ does not exceed 1+ square root p/sup n/. A complete distribution of correlation values is provided. As a special case of this construction, a previous construction due to Sidelnikov (1971) is obtained. The family of sequences is asymptotically optimum with respect to its correlation properties, and, in comparison with many previous nonbinary designs, the present design has the additional advantage of not requiring an alphabet of size larger than three. The new sequences are suitable for achieving code-division multiple access and are easily implemented using shift registers. They wee discovered through an application of Deligne's bound (1974) on exponential sums of the Weil type in, several variables. The sequences are also shown to have strong identification with certain bent functions. >