We have derived a lower bound on the linear span of a binary sequence gener
ated by a Feedback with Carry Shift Register (FCSR) under the following con
dition: q is a power of a prime such that q = r(e)(e greater than or equal
to 2) acid r (= 2p + 1), where both r and p are 2-prime. This allows us to
design FCSR stream ciphers similar to previously proposed Linear Feedback S
hift Register (LFSR) stream ciphers.