Compressed sensing is an effective compression algorithm. It is widely used to measure signals in distributed sensor networks (DSNs). Considering the limited resources of DSNs, the measurement matrices used in DSNs must be simple. In this paper, we construct a deterministic measurement matrix based on Gordon-Mills-Welch (GMW) sequence. The column vectors of the proposed measurement matrix are generated by cyclically shifting a GMW sequence. Compared with some state-of-the-art measurement matrices, the proposed measurement matrix has relative lower computational complexity and needs less storage space. It is suitable for resource-constrained DSNs. Moreover, because the proposed measurement matrix can be realized by using simple shift register, it is more practical. The simulation result shows that, in terms of recovery quality, the proposed measurement matrix performs better than some state-of-the-art measurement matrices.

Binary sequences with good autocorrelation and crosscorrelation properties are widely used in signal processing. If the autocorrelation properties are optimum, then the sequences are called perfect. In this paper we show, that the calculation of the crosscorrelation between Gordon-Mills-Welch sequences and Dillon-Dobbertin sequences is related to the crosscorrelation of m-sequences and their decimations. Furthermore, we give an upper bound for the maximum crosscorrelation coefficient (in absolute value) for certain perfect sequences.