In this thesis

we proposed a method to construct the feedback functions of the nonlinear shift registers based on three items' primary polynomial.First of all

we proved the characteristic state sets of the linear feedback shift registers with the feedback functions of three items' primary polynomial

we extracted its eigenfunction and synthesized the feedback function for the nonlinear shift register.Secondly

we implemented the non-linear feedback shift register on FPGA.Finally

we conducted analyses and calculations for new sequences generated by the nonlinear shift registers and simulated the sequences in direct sequence spread spectrum code division multiple access communication system(DS-CDMA).The results show unanimously that the new sequences dose not only possess ideal pseudorandom property and better linear complexity

but also get lower bit error rate(BER) than m sequence or gold sequence in the same communication system.