On the Cross-Correlation of a Ternary $m$-sequence of Period $3^{4k}-1$ and Its Decimated Sequence by $\frac{(3^{2k}+1{)}^2}{20}$

Abstract

Let $d=\frac{(3^{2k}+1{)}^2}{20}$, where $k$ is an odd integer. We show that the magnitude of the cross-correlation values of a ternary $m$-sequence $\{s_t\}$ of period $3^{4k}-1$ and its decimated sequence $\{s_{dt}\}$ is upper bounded by $5\sqrt{3^n}+1$, where $n=4k$.