Some new results on cross correlation of $p$-ary $m$-sequence and its decimated sequence

Wenbing  Chen; Jinquan  Luo; Yuansheng  Tang; Quanquan  Liu

doi:10.3934/amc.2015.9.375

Article Contents

2015, Volume 9, Issue 3: 375-390. Doi: 10.3934/amc.2015.9.375

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Some new results on cross correlation of $p$-ary $m$-sequence and its decimated sequence

1.
School of Mathemetics & Computation Science, Anqing Normal University, Anqing, Anhui 246133
2.
Department of Mathematic and Statistics, Centtal China Normal University, Wuhan, Hubei 430079
3.
Department of Mathematic Sciences, Yangzhou University, Yangzhou, Jiangsu 225002

Received: August 31, 2014

Published: October 2015

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Abstract

Let $p$ be an odd prime, $n=2m$, and $n/\gcd(k,n)$ be odd. In this paper, we study the cross correlation between a $p$-ary $m$-sequence $(s_{t})$ of period $p^{n}-1$ and its decimated sequence $(s_{dt})$ where $d$ satisfies $d(p^k+1)\equiv p^m+1 \pmod {p^n-1}$. Our results show that the cross-correlation function is six-valued and the distribution of the cross correlation is also completely determined.

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Mathematics Subject Classification: Primary: 94A55; Secondary:11B50.

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