On the Correlation Distribution for a Ternary Niho Decimation

Yongbo Xia; Nian Li; Xiangyong Zeng; Tor Helleseth

On the Correlation Distribution for a Ternary Niho Decimation

Information Theory 2016-12-21 v1 math.IT

Authors: Yongbo Xia , Nian Li , Xiangyong Zeng , Tor Helleseth

Abstract

In this paper, let $n=2m$ and $d=3^{m+1}-2$ with $m\geq2$ and $\gcd(d,3^n-1)=1$ . By studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over the finite field $\mathbb{F}_{3^n}$ , the correlation distribution between a ternary $m$ -sequence of period $3^n-1$ and its $d$ -decimation sequence is completely determined. This is the first time that the correlation distribution for a non-binary Niho decimation has been determined since 1976.

Cite

@article{arxiv.1612.06686,
  title  = {On the Correlation Distribution for a Ternary Niho Decimation},
  author = {Yongbo Xia and Nian Li and Xiangyong Zeng and Tor Helleseth},
  journal= {arXiv preprint arXiv:1612.06686},
  year   = {2016}
}

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