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

Overview & Synopsis

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 $1