New Optimal Quaternary Sequences with Period 2N from Interleaving Tang–Lindner Sequences

In this paper, using the interleaving technique, we present a method for constructing M-ary sequences of length 4N. We propose a new concept, referred to as the semi-interleaved sequence, based on some of the special cases of our construction. The period of these semi-interleaved sequences is 2N, and their autocorrelations can be obtained in the same way as those of interleaved sequences. Applying the construction to certain known sequences, we obtain new quaternary sequences having period 2N where N=4f+1 is prime and f is an odd integer. The nontrivial autocorrelations of the new sequences are 2 and −2. From the autocorrelation distributions, we know that the new sequences cannot be obtained by previously known methods.