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On irreducible polynomials of certain types in finite fields

Published online by Cambridge University Press:  24 October 2008

Stephen D. Cohen
Stephen D. Cohen
Affiliation:
University of Glasgow
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Let GF(q) be the finite field containing q = pl elements, where p is a prime and l a positive integer. Let P(x) be a monic polynomial in GF[q, x] of degree m. In this paper we investigate the nature and distribution of monic irreducible polynomials of the following types:

(I) P(xr), where r is a positive integer (r-polynomials).

(II) xm P(x + x−1). (Reciprocal polynomials.) These have the form

(III) xrmP(xr + x−r). (r-reciprocal polynomials.) These have the form Q(xr), where q(x) satisfies (1·1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 335 - 344
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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