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On the Number of Linear Feedback Shift Registers With a Special Structure

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2 Author(s)
Krishnaswamy, S. ; Dept. of Electr. Eng., Indian Inst. of Bombay, Mumbai, India ; Pillai, H.K.

Given a primitive polynomial , of degree , 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 . 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.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 3 )