On the Correlation Distribution for a Ternary Niho Decimation

Abstract

In this paper, let $n=2m$ and $d=3^{m+1}-2$ with $m\ge 2$ 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.