AMC
A new nonbinary sequence family with low correlation and large size
Hua Liang Wenbing Chen Jinquan Luo Yuansheng Tang
Advances in Mathematics of Communications 2017, 11(4): 671-691 doi: 10.3934/amc.2017049

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.

keywords: Sequence family m-sequence cross-correlation exponential sum
AMC
Some new results on cross correlation of $p$-ary $m$-sequence and its decimated sequence
Wenbing Chen Jinquan Luo Yuansheng Tang Quanquan Liu
Advances in Mathematics of Communications 2015, 9(3): 375-390 doi: 10.3934/amc.2015.9.375
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.
keywords: $p$-ary sequence exponential sum Cross correlation quadratic form.

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