Ternary perfect sequences with three-valued cross-correlation
Chenchen Liu, Wenyi Zhang, Yang Yang · Advances in Mathematics of Communications · 2022
The calculation of the cross-correlation between a sequence with good autocorrelation and its decimated sequence has been a longstanding research problem in the field of sequence design. The objective of this paper is to determine the cross-correlation between a class of well-known ternary sequences with perfect autocorrelation and its \begin{document}$ 2 $\end{document} -decimation. Based on the theory of quadratic forms and exponential sums over finite fields, it is shown that the cross-correlation function takes on three low values.