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

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

159
views

0
downloads

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

Suggestions

OpenMETU
Core

L-Polynomials of the Curve Özbudak, Ferruh (2014-09-28) Let chi be a smooth, geometrically irreducible and projective curve over a finite field F-q of odd characteristic. The L-polynomial L-chi(t) of chi determines the number of rational points of chi not only over F-q but also over F-qs for any integer s >= 1. In this paper we determine L-polynomials of a class of such curves over F-q.
A note on the minimal polynomial of the product of linear recurring sequences Cakcak, E (1999-08-06) Let F be a field of nonzero characteristic, with its algebraic closure, F. For positive integers a, b, let J(a, b) be the set of integers k, such that (x - 1)k is the minimal polynomial of the termwise product of linear recurring sequences sigma and tau in F ($) over bar, with minimal polynomials (x - 1)(a) and (x - 1)(b) respectively. This set plays a crucial role in the determination of the product of linear recurring sequences with arbitrary minimal polynomials. Here, we give an explicit formula to deter...
Explicit maximal and minimal curves over finite fields of odd characteristics Özbudak, Ferruh (2016-11-01) In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].
Additive polynomials and primitive roots over finite fields Özbudak, Ferruh (2001-01-01) We prove existence of primitive roots with a prescribed nonzero image using the arithmetic of algebraic function fields for a class of polynomials over sufficiently large finite fields.
Classification of function fields with class number three BİLHAN, Mehpare; Buyruk, Dilek; Özbudak, Ferruh (2015-11-01) We give the full list of all algebraic function fields over a finite field with class number three up to isomorphism. Our list consists of explicit equations of algebraic function fields which are mutually non-isomorphic over the full constant field.

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.