Abstract
Let F denote the field of rational functions over some base field. Every subspace V of F n has a polynomial basis. A polynomial basis having minimal possible degrees is called a minimal basis of V. It was shown by G.D. Forney that minimal bases always exist and that these bases are of great importance in multivariable systems theory and convolutional coding theory.
Supported in part by NSF grant DMS-96-10389. This research has been carried out while the author was a guest professor at EPFL in Switzerland. The author would like to thank EPFL for its support and hospitality.
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Rosenthal, J. (2002). Minimal Bases of Rational Vector Spaces and Their Importance in Algebraic Systems Theory. In: Blahut, R.E., Koetter, R. (eds) Codes, Graphs, and Systems. The Kluwer International Series in Engineering and Computer Science, vol 670. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0895-3_20
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