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

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Çakıroğlu Y., Yayla O., Yilmaz E. S.

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

  • 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.