# A family of sequences with large size and good correlation property arising from $M$-ary Sidelnikov sequences of period $q^d-1$ - Computer Science > Information Theory

A family of sequences with large size and good correlation property arising from $M$-ary Sidelnikov sequences of period $q^d-1$ - Computer Science > Information Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: 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$q ightarrow \infty$, of that is $\frac{ M-1q^{d-1}}{d }$. This extends thepioneering work of Yu and Gong for $d=2$ case.

Author: ** Dae San Kim**

Source: https://arxiv.org/