This paper studies the 2-adic complexity of the self-shrinking sequence under the relationship between 2-adic integers and binary sequences. Based on the linear complexity and the number of the sequences which have the same connection integer, we conclude that the 2-adic complexity of the self-shrinking sequence constructed by a binary m-sequence of order n has a lower bound 2^n-2-1. Furthermore, it is shown that its 2-adic complexity has a bigger lower bound under some circumstances.

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The approximately synchronized code-division multiple-access (CDMA) communication system, using the QAM sequences with zero correlation zone (ZCZ) as its spreading sequences, not only can remove the multiple access interference (MAI) and multi-path interference (MPI) synchronously, but also has a higher transmission data rate than the one using traditional ZCZ sequences with the same sequence length. Based on Gray mapping and the known binary ZCZ sequences, in this letter, six families of 16-QAM sequences with ZCZ are presented. When the binary ZCZ sequences employed by this letter arrive at the theoretical bound on the binary ZCZ sequences, and their family size is a multiple of 4 or 2, two of the resultant six 16-QAM sequence sets satisfy the bound referred to above as well.

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We determine the autocorrelations of the quaternary sequence over F₄ and its modified version introduced by Du et al. [X.N. Du et al., Linear complexity of quaternary sequences generated using generalized cyclotomic classes modulo 2p, IEICE Trans. Fundamentals, vol.E94-A, no.5, pp.1214-1217, 2011]. Furthermore, we reveal a drawback in the paper aforementioned and remark that the proof in the paper by Kim et al. can be simplified.

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