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Distribution of Irreducible Polynomials over F 2

In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas

Author

Listed:
  • Kenneth H. Hicks

    (Ohio University, Department of Physics)

  • Gary L. Mullen

    (The Pennsylvania State University, Department of Mathematics)

  • Ikuro Sato

    (Ohio University, Department of Physics)

Abstract

Using a polynomial analogue of the wheel sieve, we discuss the distribution of irreducible polynomials over F 2. In particular, we provide considerable numerical evidence that in analogue to integer arithmetic progressions, irreducible polynomials over F 2 are binomially distributed in the progressions of the wheel sieve. We also present, numerical evidence that the irreducibles of fixed degree are binomially distributed by weight. Also briefly discussed is the distribution of self-reciprocal irreducible polynomials. A number of conjectures are raised.

Suggested Citation

  • Kenneth H. Hicks & Gary L. Mullen & Ikuro Sato, 2002. "Distribution of Irreducible Polynomials over F 2," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 177-186, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_13
    DOI: 10.1007/978-3-642-59435-9_13
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