The Linear Span of A Binary Sequence Family with Optimal Correlation Properties

摘要

Sequences are critical for anti-jamming and security in spread spectrum communications networks. The complexity to break sequence is measured by linear span of sequence. The linear span of a sequence is the lowest degree of the characteristic polynomials that can generate the sequence. A new family of sequences with optimal correlation properties is constructed for the generalized Kasami set. A lower bound on the linear span is established. It is proved that with suitable choices of parameters, the linear span of this family is exponentially larger than that of either No sequences or TN sequences. A class of sequences with ideal autocorrelation is also proved to have large linear span. Therefore, the new family of sequences can be employed by future spread spectrum networks to have better security and lower bit error rate in the presence of jamming.