"Primitive Normal Polynomials Over Finite Fields" by Ilene H. Morgan and Gary L. Mullen
 

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

International Standard Serial Number (ISSN)

0025-5718

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1994 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 1994

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