Cyclonomials and Irreducible Polynomials over a Finite Field and their Zeros

A.J. van Zanten

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Abstract

A number of properties is derived concerning the distribution of irreducible polynomials in the ring GF(q)[x] as factors of cyclonomials. Furthermore, it is proven that the number of irreducible polynomials of degree m and with trace τ in GF(q)[x] is the same for all values of τ, if q is a prime and m is not a multiple of q. The same appears to be true if m is a multiple of q for all values of τ is not equal to 0.
Original languageEnglish
PublisherTilburg University
Number of pages31
Publication statusPublished - 2019
Externally publishedYes

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Irreducible polynomial
Galois field
Zero
Trace
Ring

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van Zanten, A.J. / Cyclonomials and Irreducible Polynomials over a Finite Field and their Zeros. Tilburg University, 2019. 31 p.
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Cyclonomials and Irreducible Polynomials over a Finite Field and their Zeros. / van Zanten, A.J.

Tilburg University, 2019. 31 p.

Research output: Book/ReportReportProfessional

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