On the construction of certain odd degree irreducible polynomials over finite fields
Designs, Codes, and Cryptography, cilt.92, sa.12, ss.4085-4097, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 92 Sayı: 12
- Basım Tarihi: 2024
- Doi Numarası: 10.1007/s10623-024-01479-7
- 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.4085-4097
- Anahtar Kelimeler: 11T06, 11T71, 12E10, 12E20, Finite fields, Hilbert Theorem 90, Irreducible polynomials
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
For an odd prime power q, let Fq2=Fq(α), α2=t∈Fq be the quadratic extension of the finite field Fq. In this paper, we consider the irreducible polynomials F(x)=xk-c1xk-1+c2xk-2-⋯-c2qx2+c1qx-1 over Fq2, where k is an odd integer and the coefficients ci are in the form ci=ai+biα with at least one bi≠0. For a given such irreducible polynomial F(x) over Fq2, we provide an algorithm to construct an irreducible polynomial G(x)=xk-A1xk-1+A2xk-2-⋯-Ak-2x2+Ak-1x-Ak over Fq, where the Ai’s are explicitly given in terms of the ci’s. This gives a bijective correspondence between irreducible polynomials over Fq2 and Fq. This fact generalizes many recent results on this subject in the literature.