$p$-ary sequences with six-valued cross-correlation function: a new decimation of Niho type

For an odd prime $p$ and $n=2m$, a new decimation $d=\frac{ (p^{ m}-1)^{ 2}}{ 2}+1$ of Niho type of $m$-sequences is presented. Using generalized Niho's Theorem, we show that the cross-correlation function between a $p$-ary $m$-sequence of period $p^{ n}-1$ and its decimated sequence by the above $d$ is at most six-valued and we can easily know that the magnitude of the cross correlation is upper bounded by $4\sqrt{ p^{ n}}-1$.

Categories: cs.IT cs.DM math.IT