Based on the number of cyclotomy of order eight, a class of balanced almost 8-QAM sequences with odd prime periods is presented. The resultant sequences have low two-level nontrivial autocorrelation values, and their distribution is determined. Furthermore, the smallest possible absolute sidelobes (SPASs) of autocorrelation functions of balanced almost 8-QAM sequences are derived. Compared with the obtained SPASs, some of the proposed sequences is optimal or suboptimal.

Perfect arrays are widely applied to high-dimensional communications, time-frequency-coding, spatial correlation or map matching, built-in tests of VLSI-circuits, radar, and so on. The letter investigates perfect arrays over the 8-QAM+ constellation, and two constructions for yielding such arrays are presented. Furthermore, the family size of the proposed arrays is determined as well.

Sequences that attain the smallest possible absolute sidelobes (SPASs) of periodic autocorrelation function (PACF) play fairly important roles in synchronization of communication systems, Large scale integrated circuit testing, and so on. This letter presents an approach to construct 16-QAM sequences of even periods, based on the known quaternary sequences. A relationship between the PACFs of 16-QAM and quaternary sequences is established, by which when quaternary sequences that attain the SPASs of PACF are employed, the proposed 16-QAM sequences have good PACF.

The shift-and-add property (SAP) of a p-ary m-sequence {ak} with period N=pn-1 means that this sequence satisfies the equation {ak+η}+{ak+τ}={ak+λ} for some integers η, τ and λ. For an arbitrarily-given p-ary m-sequence {ak}, we develop an algebraic approach to determine the integer λ for the arbitrarily-given integers η and τ. And all trinomials can be given. Our calculation only depends on the reciprocal polynomial of the primitive polynomial which produces the given m-sequence {ak}, and the cyclotomic cosets mod pn-1.