# 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…

## 9 Citations

### The cross correlation distribution of a p-ary m-sequence of period pm-1 and its decimated sequences by (pk+1)(pm+1)/4

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- Computer ScienceIEEE Transactions on Information Theory
- 2014

The cross-correlation between a p-ary m-sequence and its d-decimated sequences is investigated, and the cross correlation distribution is completely determined.

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From this result, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by −1+5p n/2 2 5 √ 2 √ N is constructed, where N = p n −1 2 is the period of sequences in the family.

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It is shown that the cross correlation takes at least four values and the validity of two famous conjectures due to Sarwate et al. and Helleseth are confirmed.

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Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these…

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