Swan-like results for binomials and trinomials over finite fields of odd characteristic

DOI10.1007/s10623-010-9476-7zbMath1248.11097OpenAlexW2028694851MaRDI QIDQ648071

Juan-Miguel Gracia

Publication date: 22 November 2011

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-010-9476-7

zbMATH Keywords

finite fieldsdiscriminantSwan's theoremnumber of factors of polynomials

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Factorization (11Y05)

Related Items (6)

Block companion singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields ⋮ Sudoku-like arrays, codes and orthogonality ⋮ A Swan-like note for a family of binary pentanomials ⋮ On polynomials \(x^n-1\) over binary fields whose irreducible factors are binomials and trinomials ⋮ A note on the stability of trinomials over finite fields ⋮ A generalization of the Hansen-Mullen conjecture on irreducible polynomials over finite fields

Cites Work

• The parity of the number of irreducible factors for some pentanomials
• A Swan-like theorem
• Parity of the number of irreducible factors for composite polynomials
• Efficient \(p\)th root computations in finite fields of characteristic \(p\)
• Factorization of polynomials over finite fields
• Factorization of trinomials over Galois fields of characteristic 2
• Integer factoring
• On the distribution of irreducible trinomials over \(\mathbb F_3\)
• Swan's theorem for binary tetranomials
• A note on the reducibility of binary affine polynomials
• Ten new primitive binary trinomials
• Irreducible trinomials over finite fields

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