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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Zeros of complete symmetric polynomials over finite fields
有限域 完全对称 多项式 零点
2023/4/13
Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. ...
Characteristic Set Algorithms for Equation Solving in Finite Fields and Applications in Cryptanalysis
Characteristic set finite field proper triangular set regular triangular set Boolean function stream cipher
2013/9/9
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula ...
Areas of triangles and Beck's theorem in planes over finite fields
Areas of triangles Beck's theorem planes over finite fields Combinatorics
2012/5/9
It is shown that any subset $E$ of a plane over a finite field $\F_q$, of cardinality $|E|>q$ determines not less than $\frac{q-1}{2}$ distinct areas of triangles, moreover once can find such triangle...
Representations of quivers with automorphisms over finite fields
quiver with automorphism hereditary algebra representation
2011/9/28
Let ${mathbb F}_q$ be the finite field of $q$ elements and $k$ be its algebraic closure. Let $Q$ be a quiver with automorphism $sigma$. In this survey we focus on the study of modules over the ${mathb...
Randomized Communication Complexity for Linear Algebra Problems over Finite Fields
communication complexity streaming, matrix singularity determinant
2012/12/3
Finding the singularity of a matrix is a basic problem in linear algebra. Chu and Schnitger first considered this problem in the communication complexity model, in which Alice holds the first half of ...
Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two
Graphs finite fields of characteristic two Number Theory
2011/9/19
Abstract: In this paper we study the structure of the graphs associated with the iterations of the map $x \mapsto x+x^{-1}$ over finite fields of characteristic two. Formulas are given for the length ...
Additive decompositions induced by multiplicative characters over finite fields
Characters Residuacity Finite Fields
2011/8/26
Abstract: In 1952, Perron showed that quadratic residues in a field of prime order satisfy certain ad- ditive properties. This result has been generalized in different directions, and our contribution...
On the tensor rank of multiplication in finite extensions of finite fields
finite fields tensor rank of multiplication Algebraic Geometry
2011/8/26
Abstract: In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite fields and we establish new asymptotical and not asymptotical upper bounds abo...
Singularity of Random Matrices over Finite Fields
Singularity of Random Matrices Finite Fields
2011/1/20
Let A be an n×n random matrix with iid entries over a finite field of order q. Suppose that the entries do not take values in any additive coset of the field with probability greater than 1 − ...
On explicit factors of Cyclotomic polynomials over finite fields
Cyclotomic polynomials finite fields
2010/11/24
We study the explicit factorization of $2^n r$-th cyclotomic polynomials over finite field $\mathbb{F}_q$ where $q, r$ are odd with $(r, q) =1$. We show that all irreducible factors of $2^n r$-th cyc...
Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields
Relatively Prime Polynomials Nonsingular Hankel Matrices
2010/11/12
The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel ma...
On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields
The Characteristic Polynomial Frobenius Supersingular Abelian
2010/11/15
In this article, we derive the list of the characteristic polynomials of the Frobenius endomorphism of simple supersingular abelian varieties of dimension $1,~2,~3,~4,~5,~6,~7$ over $\mathbb{F}_q$ whe...
Rational points over finite fields for regular models of algebraic varieties of Hodge type $\geq 1$
Rational points algebraic varieties of Hodge type $\geq 1$
2010/11/26
Let R be a discrete valuation ring of mixed characteristics (0, p), with finite residue field k and fraction field K, let k′ be a finite extension of k, and let X be a regular, proper and flat R-schem...
The minimum distance of parameterized codes of complete intersection vanishing ideals over finite fields
parameterized codes of complete intersection ideals finite fields
2010/12/13
Let X be a subset of a projective space, over a finite field K, which is parameterized by the monomials arising from the edges of a clutter. Let I(X) be the vanishing ideal of X. It is shown that I(X)...
Restriction estimates for the paraboloid over finite fields
Restriction estimates paraboloid over finite fields
2010/12/7
We prove certain endpoint restriction estimates for the paraboloid over finite fields in
three and higher dimensions. Working in the bilinear setting, we are able to pass from esti-
mates for charac...