On the Number of Linear Feedback Shift Registers With a Special Structure
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.
primitive polynomial linear feedback shift register (lfsr) linear recurring relation (lrr) m-companion matrices