On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated Sequences by d=(pn+1)/(pk+1)+(pn-1)/2

@article{Choi2012OnTC,
  title={On the Cross-Correlation of a p-Ary m-Sequence and Its Decimated Sequences by d=(pn+1)/(pk+1)+(pn-1)/2},
  author={Sung-Tai Choi and Ji-Youp Kim and Jong-Seon No},
  journal={IEICE Trans. Commun.},
  year={2012},
  volume={96-B},
  pages={2190-2197}
}
In this paper, for an odd prime $p$ such that $p\equiv 3\bmod 4$, odd $n$, and $d=(p^n+1)/(p^k+1)+(p^n-1)/2$ with $k|n$, the value distribution of the exponential sum $S(a,b)$ is calculated as $a$ and $b$ run through $\mathbb{F}_{p^n}$. The sequence family $\mathcal{G}$ in which each sequence has the period of $N=p^n-1$ is also constructed. The family size of $\mathcal{G}$ is $p^n$ and the correlation magnitude is roughly upper bounded by $(p^k+1)\sqrt{N}/2$. The weight distribution of the… 

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