Feasible calculation of the generator for combined LFSR sequences

  • Lu Peizhong
  • Song Guowen
Submitted Contributions Error Correcting Codes: Theory And Applications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)


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).

The purpose of our paper is to determine the generating polynomial of the recurrence sequences obtained by multiplying the outputs of these LFSRs. When R is a finite field, we present a new explicit and computationally feasible method for determining the polynomial h(x), without factoring the polynomials fi(x), such that
$$SR(h(x)) = SR(f1(x))...SR(fn(x))$$

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Lu Peizhong
    • 1
  • Song Guowen
    • 1
  1. 1.Telecommunication TechniquesResearch Institute ofShanghaiPeople's Republic of China

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