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

TL;DR

This paper introduces a new decimation method of Niho type for p-ary m-sequences, demonstrating that the resulting cross-correlation function is at most six-valued with a bounded magnitude, advancing sequence analysis.

Contribution

It presents a novel decimation of Niho type for p-ary m-sequences and analyzes its cross-correlation properties using generalized Niho's Theorem.

Findings

Cross-correlation function is at most six-valued.

Magnitude of cross-correlation is bounded by 4√(p^n)-1.

New decimation expands understanding of sequence correlation properties.

Abstract

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 $4\sqrt{p^{n}}-1$.