Linear complexity of a type of clock-controlled sequence

A new type of cascaded clock-controlled system is proposed. There are r+1 linear feedback shift registers (LFSRs) of length n in the system if the degree of cascade connection is r. It is proved that for an rth degree cascade the output sequences have linear complexity n Sigma _i=0^r (2ⁿ-1)ⁱ, period (2ⁿ-1)^r+1 and good statistical properties. Such a model can generate key stream sequences of stream ciphers in computer applications.