New Families of $p$-ary Sequences of Period $\frac{p^n-1}{2}$ With Low Maximum Correlation Magnitude

Wijik Lee; Ji-Youp Kim; Jong-Seon No

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arXiv · 1310.2686

New Families of $p$-ary Sequences of Period $\frac{p^n-1}{2}$ With Low Maximum Correlation Magnitude

Wijik Lee·Ji-Youp Kim·Jong-Seon No

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Abstract

Let $p$ be an odd prime such that $p \equiv 3\;{\rm mod}\;4$ and $n$ be an odd integer. In this paper, two new families of $p$-ary sequences of period $N = \frac{p^n-1}{2}$ are constructed by two decimated $p$-ary m-sequences $m(2t)$ and $m(dt)$, where $d = 4$ and $d = (p^n + 1)/2=N+1$. The upper bound on the magnitude of correlation values of two sequences in the family is derived using Weil bound. Their upper bound is derived as $\frac{3}{\sqrt{2}} \sqrt{N+\frac{1}{2}}+\frac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.

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Wijik Lee, Ji-Youp Kim, Jong-Seon No. 2013-10-10. New Families of $p$-ary Sequences of Period $\frac{p^n-1}{2}$ With Low Maximum Correlation Magnitude. https://arxiv.org/abs/1310.2686

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