On the solution of algebraic equations over finite fields
From MaRDI portal
Publication:5550482
DOI10.1016/S0019-9958(67)91016-9zbMath0166.04803OpenAlexW1990605160MaRDI QIDQ5550482
No author found.
Publication date: 1967
Published in: Information and Control (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0019-9958(67)91016-9
Related Items
Some classes of permutation polynomials of the form \(b(x^q +ax+\delta)^{\frac{i(q^2 -1)}{d}+1}+c(x^q +ax+\delta)^{\frac{j(q^2 -1)}{d}+1}+L(x)\) over \(\mathbb{F}_{q^2}\) ⋮ Bent and bent\(_4\) spectra of Boolean functions over finite fields ⋮ Some classes of permutation polynomials of the form \((x^{p^m}-x+\delta)^s+x\) over \(\mathbb{F}_{p^{2m}}\) ⋮ On the behavior of some APN permutations under swapping points ⋮ On equations of finite fields of characteristic 2 and APN functions ⋮ Non-binary irreducible quasi-cyclic parity-check subcodes of Goppa codes and extended Goppa codes ⋮ Further results on permutation polynomials from trace functions ⋮ On a conjecture of differentially 8-uniform power functions ⋮ Survey on recent trends towards generalized differential and boomerang uniformities ⋮ New classes of permutation binomials and permutation trinomials over finite fields ⋮ Are fifth-degree equations over \(GF(5^ m)\) solvable by radicals? ⋮ Further results on permutation trinomials over finite fields with even characteristic ⋮ New permutation trinomials constructed from fractional polynomials ⋮ Solids in the space of the Veronese surface in even characteristic ⋮ Decoding the triple-error-correcting (15, 5) binary BCH code by the analytic solution of the cubic error-locator polynomial over GF(24) ⋮ Several classes of complete permutation polynomials with Niho exponents ⋮ New constructions of permutation polynomials of the form \(x^rh\left( x^{q-1}\right) \) over \({\mathbb F}_{q^2}\) ⋮ Univariate polynomial factorization over finite fields ⋮ Fast algorithms for solving equations of degree \(\le 4\) in some finite fields ⋮ Necessary and sufficient conditions of two classes of permutation polynomials ⋮ On the Menezes-Teske-Weng conjecture ⋮ Several classes of permutation polynomials of the form \((x^{p^m} - x + \delta)^s + x\) over \(\mathbb{F}_{p^{2m}}\) ⋮ Partially APN functions with APN-like polynomial representations ⋮ Algebraic theory of block codes detecting independent errors ⋮ More differentially 6-uniform power functions ⋮ On a conjecture concerning Kloosterman polynomials ⋮ Complete permutation polynomials with the form \((x^{p^m} - x + \delta)^s + a x^{p^m} + b x\) over \(\mathbb{F}_{p^n}\) ⋮ Several classes of permutation polynomials over the finite field \(\mathbb{F}_{p^{2 m}}\) ⋮ Generalized Lucas polynomials over finite fields ⋮ A class of new permutation trinomials ⋮ New permutation quadrinomials over \(\mathbb{F}_{2^{2m}}\) ⋮ Infinite families of 3‐designs from APN functions ⋮ Some new results on permutation polynomials of the form \(b (x^q + ax + \delta)^s - ax\) over \(\mathbb{F}_{q^2}\) ⋮ Note on Budaghyan and Carlet's almost perfect nonlinear functions ⋮ Permutation polynomials of the form \(cx+\mathrm{Tr}_{q^l/ q}(x^a)\) and permutation trinomials over finite fields with even characteristic ⋮ New results on permutation polynomials of the form \((x^{{p}^{m}} - x + \delta)^s + x^{p^m} + x\) over \(\mathbb F_{p^{2m}}\) ⋮ Several classes of permutation polynomials based on the AGW criterion over the finite field \(\mathbb{F}_{2^{2m}}\) ⋮ On cosets of weight 4 of binary BCH codes with minimum distance 8 and exponential sums ⋮ Constructions with high algebraic degree of differentially 4-uniform \((n, n - 1)\)-functions and differentially 8-uniform \((n, n - 2)\)-functions ⋮ The cycle structure of a class of permutation polynomials ⋮ On a new identity for Kloosterman sums and nonlinear system of equations over finite fields of characteristic 2. ⋮ Two classes of permutation polynomials having the form \((x^{2^m}+x+\delta)^s+x\) ⋮ Fractional LWE: A Nonlinear Variant of LWE ⋮ More classes of permutation trinomials with Niho exponents ⋮ Investigations on \(c\)-boomerang uniformity and perfect nonlinearity ⋮ Threshold data structures and coding theory ⋮ Complete solution over \(\mathbb{F}_{p^n}\) of the equation \(X^{p^k+1}+X+a=0\) ⋮ Two-to-one mappings and involutions without fixed points over \(\mathbb{F}_{2^n}\) ⋮ Linear codes from vectorial Boolean power functions ⋮ Some new results on permutation polynomials over finite fields ⋮ Factoring Polynomials Over Large Finite Fields ⋮ The generalized Goertzel algorithm and its parallel hardware implementation ⋮ Note on cubics over \(GF(2^n)\) and \(GF(3^n)\) ⋮ A class of permutation quadrinomials ⋮ Two classes of permutation trinomials with Niho exponents ⋮ Two classes of binary cyclic codes and their weight distributions ⋮ Further results on permutation polynomials of the form \((x^{p^m} - x + \delta)^s + L(x)\) over \(\mathbb{F}_{p^{2 m}}\) ⋮ Further results on permutation polynomials of the form (xpm − x + δ)s + L(x) over 𝔽p2m ⋮ The \(c\)-differential behavior of the inverse function under the \textit{EA}-equivalence ⋮ Some new forms of permutation polynomials based on the AGW criterion ⋮ Low \(c\)-differential and \(c\)-boomerang uniformity of the swapped inverse function ⋮ A link between two classes of permutation polynomials ⋮ Divisibility properties of classical binary Kloosterman sums ⋮ THE HOLOMORPHY CONJECTURE FOR NONDEGENERATE SURFACE SINGULARITIES ⋮ New Kloosterman sums identities over \(\mathbb F_{2^m}\) for all \(m\). ⋮ Finding roots in with the successive resultants algorithm