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

Creative Commons License

Çakıroğlu Y., Yayla O., Yilmaz E. S.

DESIGNS, CODES, AND CRYPTOGRAPHY, cilt.90, sa.10, ss.2407-2417, 2022 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 90 Sayı: 10
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10623-022-01088-2
  • Dergi Adı: DESIGNS, CODES, AND CRYPTOGRAPHY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, PASCAL, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.2407-2417
  • Anahtar Kelimeler: Irreducible polynomials, Finite fields, Trace function, Algebraic curves, CURVES, ENUMERATION, GF(2)
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.