Abstract
In this paper we first extend a minimal partial realization algorithm from vector sequences to matrix sequences of equal length by means of a lattice basis reduction algorithm over polynomial rings. We also give all minimal partial realizations for such matrix sequences and a sufficient and necessary condition for the uniqueness issue. Then we improve the above algorithm to solve the minimal partial realization problem for matrix sequences of varying length.
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Acknowledgements
The author would like to thank the anonymous reviewers for their valuable suggestions and comments. The research is supported by the National Natural Science Foundation of China (Grant No. 60773141 and No.10990011) and the National 863 Project of China (Grant No. 2006AA 01Z420).
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Wang, LP. A lattice-based minimal partial realization algorithm for matrix sequences of varying length. Cryptogr. Commun. 3, 29–42 (2011). https://doi.org/10.1007/s12095-010-0037-8
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DOI: https://doi.org/10.1007/s12095-010-0037-8
Keywords
- Minimal partial realization
- Linear feedback register synthesis
- Linear complexity
- Joint linear complexity
- Linear system theory