Problems On Feedback With Carry Shift Register

Feedback with carry shift registers(FCSR),for an sequence(?) generated by an FCSR,we call it FCSR sequence.The 2 - adic complexity is the FCSR analog of the linear complexity,so 2 - adic complexity is very useful in the study of the security of stream ciphers for cryptographic applications.In this paper,we obtain some results using a new method:The expected value and the variance of the 2 - adic complexity of FCSR sequences with connection integer q;and upper bounds on them are also given;In some case,a FCSR sequence can divide into some l-sequences sum with carry;In particular,we give upper and lower bounds of 2 - adic complexity for the sum-with-carry sequences.