A family of sequences with large size and good correlation property arising from $M$-ary Sidelnikov sequences of period $q^d-1$

摘要

Let $q$ be any prime power and let $d$ be a positive integer greater than 1.In this paper, we construct a family of $M$-ary sequences of period $q-1$ froma given $M$-ary, with $M|q-1$, Sidelikov sequence of period $q^d-1$. Under mildrestrictions on $d$, we show that the maximum correlation magnitude of thefamily is upper bounded by $(2d -1) \sqrt { q }+1$ and the asymptotic size, as$q\rightarrow \infty$, of that is $\frac{ (M-1)q^{d-1}}{d }$. This extends thepioneering work of Yu and Gong for $d=2$ case.