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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Berlekamp, E. R.: Factoring polynomials over finite fields. Bell System Technical J.46, 1853–1859 (1967)
Miller, V.: Berlekamp versus Niederreiter, preprint
Niederreiter, H.: A New Efficient Factorization Algorithm for Polynomials over Small Finite Fields. AAECC4, 81–87 (1993)
Niederreiter, H.: Factorization of polynomials and some linear algebra problems over finite fields. Linear Algebra Appl. (to appear)
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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