A new nonbinary sequence family with low correlation and large size

Hua Liang; Wenbing Chen; Jinquan Luo; Yuansheng Tang

doi:10.3934/amc.2017049

Article Contents

2017, Volume 11, Issue 4: 671-691. Doi: 10.3934/amc.2017049

This issue Previous Article Duursma's reduced polynomial Next Article On cross-correlation of a binary $m$-sequence of period $2^{2k}-1$ and its decimated sequences by $(2^{lk}+1)/(2^l+1)$

A new nonbinary sequence family with low correlation and large size

1.
School of Mathematical Sciences, Huaiyin Normal University, Huaian 223300, China
2.
School of Mathematics & Computation Science, Anqing Normal University, Anqing 246133, China
3.
School of Mathematics and Statistics, & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
4.
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

* Corresponding author
* Corresponding author

Received: May 2015

Revised: February 2016

Published: July 2018

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Abstract

Let $p$ be an odd prime, $n≥q3$ and $k$ positive integers with $e=\gcd(n,k)$ . In this paper, a new family $\mathcal{S}$ of $p$ -ary sequences with period $N=p^n-1$ is proposed. The sequences in $\mathcal{S}$ are constructed by adding a $p$ -ary sequence to its two decimated sequences with different phase shifts. The correlation distribution among sequences in $\mathcal{S}$ is completely determined. It is shown that the maximum magnitude of nontrivial correlations of $\mathcal{S}$ is upper bounded by $p^e\sqrt{N+1}+1$ , and the family size of $\mathcal{S}$ is $N^2$ . Our sequence family has a large family size and low correlation.

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Mathematics Subject Classification: Primary: 94A55; Secondary: 11T71.

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References

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