The Number of Irreducible Polynomials Over Finite Fields With Vanishing Trace and Reciprocal Trace
Loading...
Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Open Access Color
Green Open Access
Yes
OpenAIRE Downloads
OpenAIRE Views
Publicly Funded
No
BIP! Indicators
Impulse
Average
Influence
Average
Popularity
Average
Abstract
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.
Description
YAYLA, Oguz/0000-0001-8945-2780
Keywords
Irreducible polynomials, Finite fields, Trace function, Algebraic curves, FOS: Computer and information sciences, Computer Science - Cryptography and Security, Mathematics - Number Theory, Computer Science - Information Theory, Information Theory (cs.IT), FOS: Mathematics, 11T06, 11G20, 94A55, Number Theory (math.NT), Cryptography and Security (cs.CR), algebraic curves, irreducible polynomials, Polynomials over finite fields, Curves over finite and local fields, finite fields, trace function
Fields of Science
0102 computer and information sciences, 0101 mathematics, 01 natural sciences
Citation
WoS Q
Q2
Scopus Q
Q3
OpenCitations Citation Count
1
Source
Designs, Codes and Cryptography
Volume
90
Issue
10
Start Page
2407
End Page
2417
PlumX Metrics
Citations
Scopus : 1
SCOPUS™ Citations
1
checked on Apr 25, 2026
Web of Science™ Citations
1
checked on Apr 25, 2026
Google Scholar™
