Finite Fields and Their Applications

Article	Citations
LCD codes from tridiagonal Toeplitz matrices	35
On construction and (non)existence of c-(almost) perfect nonlinear functions	27
On oriented supersingular elliptic curves	21
A family of permutation trinomials over F	19
On the minimum weights of binary LCD codes and ternary LCD codes	18
Solving X+1 + X + a = 0 over finite fields	16
The parameters of minimal linear codes	15
More classes of permutation quadrinomials from Niho exponents in characteristic two	15
Flag codes from planar spreads in network coding	14
Application of Hermitian self-orthogonal GRS codes to some quantum MDS codes	13
Polycyclic codes as invariant subspaces	13
Additive cyclic complementary dual codes over F	12
Group codes over fields are asymptotically good	12
Extending two families of maximum rank distance codes	12
Constructions of near MDS codes which are optimal locally recoverable codes	11
Few-weight codes over a non-chain ring associated with simplicial complexes and their distance optimal Gray image	11
Two classes of permutation trinomials with Niho exponents	11
Further results on optimal ternary cyclic codes	11
Two-to-one mappings and involutions without fixed points over F	10
Existence of primitive 2-normal elements in finite fields	10
On the clique number of Paley graphs of prime power order	10
Permutation polynomials of the form x + L(x) over F	10
Weight distributions and weight hierarchies of two classes of binary linear codes	9
Two classes of permutation trinomials with Niho exponents over finite fields with even characteristic	9
Correlation measure, linear complexity and maximum order complexity for families of binary sequences	9

On the constructions of n-cycle permutations	9
A class of almost MDS codes	9
On 2-dimensional insertion-deletion Reed-Solomon codes with optimal asymptotic error-correcting capability	9
On pencils of cubics on the projective line over finite fields of characteristic >3	8
Two families of optimal ternary cyclic codes with minimal distance four	8
An orbital construction of optimum distance flag codes	8
Derivations of group rings for finite and FC groups	8
Multi-orbit cyclic subspace codes and linear sets	8
On trinomials of type X+(1 + AX(−1) + BX(−1)), n, m odd, over F	8
New classes of permutation trinomials over F	8
On a type of permutation rational functions over finite fields	8
Investigating the exceptionality of scattered polynomials	7
Classification of fractional projective permutations over finite fields	7
Several classes of permutation polynomials of the form (	7
Several classes of linear codes with few weights from the closed butterfly structure	7
On the differential properties of the power mapping x	7
A further study of quadratic APN permutations in dimension nine	7
Several classes of complete permutation polynomials with Niho exponents	6
Two-point AG codes from the Beelen-Montanucci maximal curve	6
Constructions of cyclic codes and extended primitive cyclic codes with their applications	6
Flag codes of maximum distance and constructions using Singer groups	6
New point compression method for elliptic F	6
Super-regular Steiner 2-designs	6
The c-differential uniformity and boomerang uniformity of three classes of permutation polynomials over	5
On incidence bounds with Möbius hyperbolae in positive characteristic	5
New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction	5
New Galois hulls of generalized Reed-Solomon codes	5
Several classes of complete permutation polynomials over finite fields of even characteristic	5
On eigenfunctions and maximal cliques of generalised Paley graphs of square order	5
Classification of quadratic APN functions with coefficients in F	5
Sum-rank product codes and bounds on the minimum distance	5
Hulls of cyclic serial codes over a finite chain ring	5
On intersection density of transitive groups of degree a product of two odd primes	5
Complete solution over F	5
On a conjecture on permutation rational functions over finite fields	5
On the constructions of Zp	5
On special pairs of primitive elements over a finite field	4
On the Grassmann graph of linear codes	4
On non-monomial APcN permutations over finite fields of even characteristic	4
Elliptic curves overFp<	4
Bases of Riemann–Roch spaces from Kummer extensions and algebraic geometry codes	4
Almost affinely disjoint subspaces	4
Hulls of double cyclic codes	4
On r-primitive k-normal elements over finite fields	4
Newton polygons of L-functions associated to Deligne polynomials	4
On the number of zeros to the equation f(x1)+... + f(x)=a over finite fields	4
Simplified isogeny formulas on twisted Jacobi quartic curves	4
Splitting subspaces of linear operators over finite fields	4
New generalized almost perfect nonlinear functions	4
Two new classes of projective two-weight linear codes	4

More results on hulls of some primitive binary and ternary BCH codes	4
Galois hulls of special Goppa codes and related codes with application to EAQECCs	4
Linear sets from projection of Desarguesian spreads	4
On binary locally repairable codes with distance four	4
A multivariate cryptosystem inspired by random linear codes	4
Weierstrass semigroups on the Skabelund maximal curve	4
A necessary and sufficient condition for a class of nonsingular Galois NFSRs	4
Five infinite families of binary cyclic codes and their related codes with good parameters	4
Investigations of c-differential uniformity of permutations with Carlitz rank 3	4
Some basic results on finite linear recurring sequence subgroups	4
Extending two families of bivariate APN functions	4
Hasse polynomials of L-functions of certain exponential sums	3
Primitive elements with prescribed traces	3
Weight distributions of generalized quasi-cyclic codes over F	3
Additive G-codes over Fq	3
A structure theorem for finite fields	3
Some sum-product estimates in matrix rings over finite fields	3
Explicit equations for maximal curves as subcovers of the BM curve	3
Roos bound for skew cyclic codes in Hamming and rank metric	3
On the error-correcting pair for MDS linear codes with even minimum distance	3
On a classification of the automorphism groups of polarized abelian surfaces over finite fields	3
The probability of spanning a classical space by two non-degenerate subspaces of complementary dimensions	3
Subconstituents of unitary Cayley graph of matrix algebras	3
Counting irreducible polynomials with prescribed coefficients over a finite field	3
On ⁎-clean group rings over finite fields	3
An asymptotically optimal construction of almost affinely disjoint subspaces	3
New Wilson-like theorems arising from Dickson polynomials	3
Solving X2	3
Coset-wise affine functions and cycle types of complete mappings	3
Classification of 9-dimensional trilinear alternating forms over GF(2)	3
Analogues of Alladi's formula over global function fields	3
New differentially 4-uniform permutations from modifications of the inverse function	3
Metrical properties for continued fractions of formal Laurent series	3
On some conjectures on generalized quadratic Gauss sums and related problems	3
A general construction of permutation polynomials of F	3
An infinite family of Griesmer quasi-cyclic self-orthogonal codes	3
Classifications and constructions of minimum size linear sets on the projective line	3
Primitive normal pairs with prescribed norm and trace	3
Partially scattered linearized polynomials and rank metric codes	3
A formula on the weight distribution of linear codes with applications to AMDS codes	3
A Bertini type theorem for pencils over finite fields	3
On equivalence between known polynomial APN functions and power APN functions	3
Linearity and classification of Z	3
Counting solutions of special linear equations over finite fields	3
Hamming weight enumerators of multi-twisted codes with at most two non-zero constituents	3
On diagonal equations over finite fields	3
The minimal polynomials of modified de Bruijn sequences revisited	3
Frames over finite fields: Basic theory and equiangular lines in unitary geometry	3
Doubly and triply extended MSRD codes	3
The number of solutions of diagonal cubic equations over finite fields	3
On enumeration of irreducible polynomials and related objects over a finite field with respect to their trace and norm	3
On diagonal equations over finite fields via walks in NEPS of graphs	3
New examples of maximal curves with low genus	3
New results on permutation binomials of finite fields	3
Symmetric polynomials over finite fields	2
Invariant rational functions, linear fractional transformations and irreducible polynomials over finite fields	2
Complete weight enumerators for several classes of two-weight and three-weight linear codes	2
A structural attack to the DME-(3,2,q) cryptosystem	2
Further improvements to the Chevalley-Warning theorems	2
Four infinite families of ternary cyclic codes with a square-root-like lower bound	2
Classification of some quadrinomials over finite fields of odd characteristic	2
The additive index of polynomials over finite fields	2
Stabilizer quantum codes defined by trace-depending polynomials	2
Completing the determination of the next-to-minimal weights of affine cartesian codes	2
A class of linear sets in PG(1,q5)	2
Pure Gauss sums and skew Hadamard difference sets	2
Generic Newton polygons for L-functions of (A,B)-exponential sums	2
The syndromes decoding algorithm in group codes	2
Permutation properties of Dickson and Chebyshev polynomials with connections to number theory	2
On the differential spectrum of a differentially 3-uniform power function	2
Del Pezzo surfaces over finite fields	2
Constructions of optimal Hermitian self-dual codes from unitary matrices	2
Energy bounds, bilinear forms and their applications in function fields	2
Perfect linear complexity profile and apwenian sequences	2
On additive MDS codes with linear projections	2
Covers of generalized quadrangles, 2. Kantor-Knuth covers and embedded ovoids	2
On sums and products of combinatorial cubes	2
Cyclotomic matrices and hypergeometric functions over finite fields	2
Moments of quadratic Dirichlet L-functions over function fields	2
Enumeration of self-reciprocal irreducible monic polynomials with prescribed leading coefficients over a finite field	2

Character sums over elements of extensions of finite fields with restricted coordinates	2
Hamming distances of constacyclic codes of length 3p and optimal codes with respect to the Griesmer and Singleton bounds	2
Linear codes associated to symmetric determinantal varieties: Even rank case	2
Appell series over finite fields and modular forms	2
Several classes of Galois self-orthogonal MDS codes and related applications	2
On the subset sum problem for finite fields	2
Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus	2
Configurations of rectangles in F	2
A note on character sums in function fields	2
A note on semi-orthogonal (G-matrix) and semi-involutory MDS matrices	2
On nested code pairs from the Hermitian curve	2
Necessary and sufficient conditions of two classes of permutation polynomials	2
Fractional decoding of r-Hermitian codes	2
On a generalization of Jacobi sums	2
Completely characterizing a class of permutation quadrinomials	2
Divisibility on point counting over finite Witt rings	2
Bounds for two multicolor Ramsey numbers concerning quadrilaterals	2
Character sums over affine spaces and applications	2
Solving some affine equations over finite fields	2
A new result on irreducible NFSRs with respect to cascade connection	2
On exponential sums of x + λx with p ≡ e(mod d)	2
On monomial generalized almost perfect nonlinear functions	2
An algebraic attack to the Bluetooth stream cipher E0	2
Several families of binary cyclic codes with good parameters	2
Bounds in the Lee metric and optimal codes	2
A new class of generalized almost perfect nonlinear power function	2
On the boomerang uniformity of permutations of low Carlitz rank	2
Dynamics on the number of prime divisors for additive arithmetic semigroups	2
F-valued trace of a finite-dimensional commutative	2
Jacobsthal sums and permutations of biquadratic residues	2
Some new constructions of MDS self-dual codes over finite fields	2
Permutation binomials of the form x(x−1 + a) over F	2
On the constructions of MDS self-dual codes via cyclotomy	2
Classification of flocks of the quadratic cone in PG(3,64)	2
Centralized variant of the Li criterion on functions fields	2
Paley-like graphs over finite fields from vector spaces	2
On a family of 2-automatic sequences generating algebraic continued fractions in characteristic 2	2
A tight upper bound on the number of non-zero weights of a constacyclic code	2
Near-MDS codes from maximal arcs in PG(2,q)	2
Rédei permutations with the same cycle structure	2
On the number of Diophantine m-tuples in finite fields	2
On subgroup perfect codes in Cayley sum graphs	2
Point-line incidence on Grassmannians and majority logic decoding of Grassmann codes	2
An explicit expression for Euclidean self-dual cyclic codes of length 2 over Galois ring GR(4,m)	2
A new identity of Dickson polynomials	2
Constructing differentially 4-uniform involutions over F	1
Negative Latin square type partial difference sets in nonabelian groups of order 64	1
On the proportion of transverse-free plane curves	1
Existence of pencils with nonblocking hypersurfaces	1
Estimates on the number ofFq	1
Higher Grassmann codes II	1
Maximality of Ciani curves over finite fields	1
Quasi-balanced weighing matrices, signed strongly regular graphs and association schemes	1
On cohomology of generalized Suzuki curves and exponential sums	1
Several classes of exponential sums and three-valued Walsh spectrums over finite fields	1
Singleton-optimal LRCs and perfect LRCs via cyclic and constacyclic codes	1
Solids in the space of the Veronese surface in even characteristic	1
Higher Grassmann codes	1
Some results on similar configurations in subsets of F	1
Saturating linear sets of minimal rank	1
RS-like locally recoverable codes with intersecting recovering sets	1
Theory of additive complementary dual codes, constructions and computations	1
Galois lines for the Artin–Schreier–Mumford curve	1
On the existence and construction of maximum distance profile convolutional codes	1
Classification of spreads of Tits quadrangles of order 64	1
On the graph of non-degenerate linear [n,2]2 codes	1
A note on the distribution of weights of fixed-rank matrices over the binary field	1
On primitive elements of finite fields avoiding affine hyperplanes	1
On the relative growth rate of the product of consecutive partial quotients in continued fraction expansions of Laurent series	1
Counting polynomials over finite fields with prescribed leading coefficients and linear factors	1
Two-weight or three-weight binary linear codes from cyclotomic mappings	1
On the Rosenhain forms of superspecial curves of genus two	1
Classifying planar monomials over fields of order a prime cubed	1
Constructions of projective linear codes by the intersection and difference of sets	1
Metrical properties for the weighted sums of degrees of multiple partial quotients in continued fractions of Laurent series	1
A note on bilinear exponential sums in prime fields	1
On the eighth power mean of the two-term exponential sums	1
Several classes of permutation polynomials over the finite field F	1
New singly and doubly even binary [72,36,12] self-dual codes from M2(R)G - group matrix rings	1
Spectral properties of Cayley graphs over M×(F)	1
Sequence subgroups generated by lifting	1
The weight enumerators of singly-even self-dual [88,44,14] codes and new binary self-dual [68,34,12] and [88,44,14] codes	1
The radical of binary dimensional dual hyperovals	1
Pseudorandom vector generation using elliptic curves and applications to Wiener processes	1
A note on the intersection of two distinct constacyclic codes	1
On the construction of irreducible and primitive polynomials from F	1
Additive one-rank hull codes over finite fields	1
Linear families of smooth hypersurfaces over finitely generated fields	1
Two classes of permutation trinomials over F	1
Self-orthogonal codes over Z4	1
Cardinal rank metric codes over Galois rings	1
How to construct CSIDH on Edwards curves	1
Averages and maximal averages over Product j-varieties in finite fields	1
The extended codes of some linear codes	1
On a girth–free variant of the Bourgain–Gamburd machine	1