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

Dae San Kim

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arXiv · 1009.1225

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

Dae San Kim

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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 $q-1$ from a given $M$-ary, with $M|q-1$, Sidelikov sequence of period $q^d-1$. Under mild restrictions on $d$, we show that the maximum correlation magnitude of the family 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 the pioneering work of Yu and Gong for $d=2$ case.

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Dae San Kim. 2010-09-07. A family of sequences with large size and good correlation property arising from $M$-ary Sidelnikov sequences of period $q^d-1$. https://arxiv.org/abs/1009.1225

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