Feasible calculation of the generator for combined LFSR sequences
We have a finite number of linear feedback shift registers (LFSR) with known generating polynomials over a commutative ring R. SR (f(x)) denotes the R module of all homogeneous LFSR sequences in R generated by f(x).
To this end we apply tensor products of matrices. We find that the polynomial h(x) is just the minimal polynomial of the tensor product of these companion matrices of fi(x).
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- N. Zierler and W. H. Mills, Products of Linear Recurring Sequences, Journal of Algebra, vol 27, 147–157 (1973)Google Scholar
- R. Lidl, Finite Fields, Addison Wesley, 1983Google Scholar
- R. A. Rueppel and O. J. Staffelbach, Products of Linear Recurring Sequences with Maximum Complexity. IEEE Trans. IT, vol33, pp124–131, 1987.Google Scholar
- S. M. Jennings, Multiplexed Sequences:Some Properties of the minimun polynomial. Crypoto'83Google Scholar
- (5).N. Jacobson, Basic Algebra II, W. H. Freeman and Company, 1980.Google Scholar