For instance, a sequence with (potentially huge) period $N=2^n-1$ can be constructed from a LFSR with only $n$ stages. The linear feedback shift register, most often used in hardware designs, is the basis of the stream ciphers we will examine here. LFSR only, and the key stream is generated from nonlinear Boolean. I now wonder if we can now say anything about the minimal FSR that outputs a given sequence. Keywords: LFSR, Chaotic Map, PRNG, Chaotic Binary Sequence Generator. Serial LFSR is used as test pattern generator in BIST.
Can that be generalized to any $N$?ĮDIT 2: So, my question was trivial, see joriki's answer below. The repeating sequence of states of an LFSR allows it to be used as a clock divider, or as a counter when a non-binary sequence is acceptable as is often the. Abstract- Linear feedback shift registers have many applications. In other words, if a binary sequence has period $N=2^n-1$ for some $n$, there exists a Linear FSR with that ouputs this sequence. From a mathematical point of view, such a sequence is constructed recursively as follows: each state of the LFSR with length at most $n$ (such a state is an element of $^n$ (Golomb, Gong, Signal Design for Good Correlation, 2005). Quick background: The output of a Linear Feedback Shift Register (LFSR) with length $n$ is a binary sequence which is periodic of length dividing $2^n-1$.
