A class of Niho type four-valued cross-correlation functions between sequences of different periods

arXiv:2610.34010v1 Announce Type: new Abstract: Determining the cross-correlation distributions between $m$-sequences and their decimated sequences is an important problem in sequence design. For two positive integers $n$ and $k$ with $n=2k$, this paper investigates the cross-correlation function between a binary $m$-sequence $\{u(t)\}$ of period $2^{n}-1$ and its $2^{\gcd(s,k)}+1$ short-period decimated sequences $\{u(dt+l)\}$, where the decimation $d=\frac{2^s}{2^s+1}(2^k-1)+1$ satisfies $1v_2(k)$. The cross-correlation function is proved to be four-valued and its value distribution is completely determined. Several previously known binary cross-correlation functions are included in our result as special cases.