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Discriminants and the irreducibility of a class of polynomials

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Applied Algebra, Algorithmics and Error-Correcting Codes (AAECC 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 228))

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Abstract

There has been some interest in finding irreducible polynomial of the type f(A(x)) for certain classes of linearized polynomials A(x) (see [1], [2], [3], [6],) over a finite field GF(pm). The main result of this paper proves the stronger result that there are no further irreducible cases of f(A(x)) fon an extended class that contains that of linearized polynomials, but for p=2. In order to reach this result, and also of independent interest, the discriminant and the parity of the factors of polynomials f(A(x)) is computed.

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Bibliography

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Authors and Affiliations

  1. Department of Mathematics, University of Puerto Rico, Río Piedras, Puerto Rico

    Oscar Moreno de Ayala

Authors
  1. Oscar Moreno de Ayala
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Editor information

Alain Poli

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© 1986 Springer-Verlag Berlin Heidelberg

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de Ayala, O.M. (1986). Discriminants and the irreducibility of a class of polynomials. In: Poli, A. (eds) Applied Algebra, Algorithmics and Error-Correcting Codes. AAECC 1984. Lecture Notes in Computer Science, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16767-6_63

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  • DOI: https://doi.org/10.1007/3-540-16767-6_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16767-9

  • Online ISBN: 978-3-540-38813-5

  • eBook Packages: Springer Book Archive

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