The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace

Date

2022-08-01

Author

Çakıroğlu, Yağmur
Yayla, Oğuz
Yılmaz, Emrah Sercan

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We present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.

Subject Keywords

Irreducible polynomials, Finite fields, Trace function, Algebraic curves, CURVES, ENUMERATION, GF(2)

URI

https://doi.org/10.1007/s10623-022-01088-2
https://hdl.handle.net/11511/99031

Journal

DESIGNS, CODES, AND CRYPTOGRAPHY

DOI

https://doi.org/10.1007/s10623-022-01088-2

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

Y. Çakıroğlu, O. Yayla, and E. S. Yılmaz, “The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace,” DESIGNS, CODES, AND CRYPTOGRAPHY, vol. 1, no. 1, pp. 1–1, 2022, Accessed: 00, 2022. [Online]. Available: https://doi.org/10.1007/s10623-022-01088-2.