Title

Primitive Normal Polynomials Over Finite Fields

Abstract

In this note we significantly extend the range of published tables of primitive normal polynomials over finite fields. For each with , we provide a primitive normal polynomial of degree n over . Moreover, each polynomial has the minimal number of nonzero coefficients among all primitive normal polynomials of degree n over . The roots of such a polynomial generate a primitive normal basis of over , 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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

finite field; primitive normal basis

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1994 American Mathematical Society, All rights reserved.

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