Ternary perfect sequences with three-valued cross-correlation

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-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.</p>

Pairs of Ternary Perfect Sequences with Three-Valued Cross-Correlation

“…Shedd and Sarwate proposed a construction of ternary perfect sequences based on m-sequences [1]. Recently, Liu et al studied the cross-correlation of the ternary sequences with perfect autocorrelation, proposed by Ipatov [29], and its 2-decimation [30].…”

“…Motivated by the works of [9] and [30], in this letter, we study the cross-correlation between the ternary sequences of length p m − 1 with perfect autocorrelation, proposed by Shedd and Sarwate [1], which are generated with different d-decimations, where…”