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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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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.