A New Family of $p$-Ary Sequences With Low Correlation Constructed From Decimated Sequences
Yongbo Xia, Shaoping Chen · IEEE Transactions on Information Theory · 2012
In this paper, for an odd prime$p$and an integer$n \geq 3$, a new family of$p$-ary sequences of period${{p^{n}-1} \over {2}}$with low correlation is constructed. The new family is constructed by shifts and additions of two decimated sequences of a$p$-ary$m$-sequence, and its family size is$2(p^{n}-1)$. The complete correlation distribution of this new family is derived. It is also shown that the family is optimal with respect to the parameter$\theta_{{\rm rms}}$, which denotes the root mean square of all nontrivial correlations. Compared with the known sequence families, our sequence family is new and has a larger family size, which is four times of its period.