4-Adic Complexity of Interleaved Quaternary Sequences

by   Shiyuan Qiang, et al.
Tsinghua University
NetEase, Inc

Tang and Ding <cit.> present a series of quaternary sequences w(a, b) interleaved by two binary sequences a and b with ideal autocorrelation and show that such interleaved quaternary sequences have optimal autocorrelation. In this paper we consider the 4-adic complexity FC_w(4) of such quaternary sequence w=w(a, b). We present a general formula on FC_w(4), w=w(a, b). As a direct consequence, we get a general lower bound FC_w(4)≥log_4(4^n-1) where 2n is the period of the sequence w. By taking a and b to be several types of known binary sequences with ideal autocorrelation (m-sequences, twin-prime, Legendre, Hall sequences and their complement, shift or sample sequences), we compute the exact values of FC_w(4), w=w(a, b). The results show that in most cases FC_w(4) reaches or nearly reaches the maximum value log_4(4^2n-1).


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