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Codebooks with low-coherence have wide utilization in code division multiple access (CDMA) communications,quantum information theory,compressed sensing and so on.In order to expand the number of codebooks,the restrictions on the transformation matrix were relaxed.Based on the Zadoff-Chu matrix,new codebooks were constructed using the difference set,almost difference set,and finite field character sum.The proposed codebooks were optimal or near optimal according to the Welch bound or Levenstein bound.Through experimental simulation,it is found that the deterministic measurement matrices constructed using these codebooks also have good performance in the process of compressed sensing.

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Let N be the odd number and ZN be the residual class ring of modular N,the paper obtains the main results as follows: (1) If D is a... difference set over...?then its autocorrelation value is four-valued. If two special points are removed, the sequence is optimal. (2) If D is a...then its autocorrelation value is six-valued. Finally, this paper also gives the autocorrelation values of a sequence of periodic 4N. [ABSTRACT FROM AUTHOR]

In this paper, divisible difference set pairs are studied. By using difference set, difference set pairs and cyclotomic class, several classes of divisible difference set pairs are constructed. It not only expands the existence space of almost perfect binary sequences pairs, but also provides broader choice range of the address codes. [ABSTRACT FROM AUTHOR]