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

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

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 ∈ F q...

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Veröffentlicht in:Designs, codes, and cryptography codes, and cryptography, 2022, Vol.90 (10), p.2407-2417
Hauptverfasser: Çakıroğlu, Yağmur, Yayla, Oğuz, Yılmaz, Emrah Sercan
Format: Artikel
Sprache:eng
Schlagworte:
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Fields (mathematics)
Mathematical analysis
Polynomials
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Beschreibung
Zusammenfassung: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 ∈ F q n for which Trace ( a ) = 0 and Trace ( a - 1 ) = 0 .
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-022-01088-2