Irreducible polynomials over finite fields with prescribed trace/prescribed constant term

Authors:
Joseph L. Yucas
Affiliations:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA
Venue:
Finite Fields and Their Applications
Year:
2006

Citing 2
Cited 3

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Abstract

We obtain an equivalent version of Carlitz's formula for the number of monic irreducible polynomials of degree n and trace @c0 over a finite field via an integer recurrence. Similar expressions for the @c=0 case are also given. We also obtain formulas for the number of monic irreducible polynomials of degree n and prescribed constant term.