On permutation polynomials of prescribed shape

DOI10.1016/j.ffa.2008.12.001zbMath1220.11145OpenAlexW2032009701MaRDI QIDQ1011450

Dragos Ghioca, Amir Akbary, Qiang Wang

Publication date: 8 April 2009

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2008.12.001

zbMATH Keywords

finite fieldspermutation polynomials

Mathematics Subject Classification ID

Polynomials over finite fields (11T06)

Related Items

The extended Laguerre polynomials \(\{A_{q, n}^{(\alpha)}(x)\}\) involving \(_qF_q\), \(q>2\) ⋮ Index bounds for character sums of polynomials over finite fields ⋮ A note on inverses of cyclotomic mapping permutation polynomials over finite fields ⋮ Enumerating permutation polynomials ⋮ On the infiniteness of a family of APN functions ⋮ The additive index of polynomials over finite fields ⋮ Permutation binomials of the form \(x^r (x^{q-1} +a)\) over \(\mathbb{F}_{q^e}\) ⋮ On the inverses of some classes of permutations of finite fields ⋮ Further results on complete permutation monomials over finite fields ⋮ The \(K\) extended Laguerre polynomials involving \(\left\{A^{(\alpha)}_{r, n, k}(x)\right\}{}_rf_r\), \(r > 2\) ⋮ Cyclotomy and permutation polynomials of large indices ⋮ Compositional inverses of permutation polynomials of the form \(x^rh(x^s)\) over finite fields ⋮ Compositional inverses and complete mappings over finite fields ⋮ Counting invariant subspaces and decompositions of additive polynomials ⋮ A probabilistic approach to value sets of polynomials over finite fields ⋮ On the constructions of \(n\)-cycle permutations ⋮ Permutation polynomials over finite fields -- a survey of recent advances ⋮ On inverse permutation polynomials ⋮ On the index of the Diffie-Hellman mapping ⋮ Further improvement on index bounds

Cites Work

• Schur covers and Carlitz's conjecture
• Enumerating permutation polynomials over finite fields by degree. II
• Permutation polynomials and applications to coding theory
• Permutation polynomials of the form \(x^r f(x^{(q-1)/d)}\) and their group structure
• Circular Tuscan-\(k\) arrays from permutation binomials
• The number of permutation polynomials of a given degree over a finite field
• Enumerating permutation polynomials over finite fields by degree
• Interleavers for turbo codes using permutation polynomials over integer rings
• When Does a Polynomial Over a Finite Field Permute the Elements of the Field?
• Permutation Polynomials in RSA-Cryptosystems
• Permutation binomials over finite fields
• The number of solutions of a special system of equations in a finite field
• On the Riemann Hypothesis in Function-Fields