On the Number of Linear Feedback Shift Registers With a Special Structure
Srinivasan Krishnaswamy, Harish K. Pillai · IEEE Transactions on Information Theory · 2011
Given a primitive polynomial$p(x)$, of degree$n$, we deal with the problem of finding the number of possible linear feedback shift register realizations, with m-input m-output delay elements, such that the corresponding characteristic polynomial is$p(x)$. We show the equivalence between these realizations and a set of specially structured matrices. Furthermore, the number of realizations is computed for some special cases.