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Subspaces and polynomial factorizations over finite fields

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Abstract

Recently Niederreiter described a new method for factoring polynomials over finite fields. As with the Berlekamp technique, the method requires the construction of a linear subspace whose dimension is precisely the number of irreducible factors of the polynomial being considered. This paper explores the connection between these subspaces and gives a characterization of other subspaces having properties which are similar.

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References

  1. Berlekamp, E. R.: Factoring polynomials over finite fields. Bell System Technical J.46, 1853–1859 (1967)

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  3. Niederreiter, H.: A New Efficient Factorization Algorithm for Polynomials over Small Finite Fields. AAECC4, 81–87 (1993)

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  4. Niederreiter, H.: Factorization of polynomials and some linear algebra problems over finite fields. Linear Algebra Appl. (to appear)

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Therese C. Y. Lee & Scott A. Vanstone

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  1. Therese C. Y. Lee
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  2. Scott A. Vanstone
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Lee, T.C.Y., Vanstone, S.A. Subspaces and polynomial factorizations over finite fields. AAECC 6, 147–157 (1995). https://doi.org/10.1007/BF01195333

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  • DOI: https://doi.org/10.1007/BF01195333

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