Primitive normal polynomials over finite fields

Ilene H. Morgan, Gary L. Mullen

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

In this note we significantly extend the range of published tables of primitive normal polynomials over finite fields. For each p" < 1050 with P < 97, we provide a primitive normal polynomial of degree n over Fp. Moreover, each polynomial has the minimal number of nonzero coefficients among all primitive normal polynomials of degree n over Fp. The roots of such a polynomial generate a primitive normal basis of Fpn over Fp, and so are of importance in many computational problems. We also raise several conjectures concerning the distribution of such primitive normal polynomials, including a refinement of the primitive normal basis theorem.

Original languageEnglish (US)
Pages (from-to)759-765
Number of pages7
JournalMathematics of Computation
Volume63
Issue number208
DOIs
StatePublished - 1994

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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