Let $E \\subset {\\Bbb F}_q^d$, the $d$-dimensional vector space over a finite field with $q$ elements. Construct a graph, called the distance graph of $E$, by letting the vertices be the elements of $E$ and connect a pair of vertices corresponding to vectors $x,y \\in E$...
摘要: We prove that a sufficiently large subset of the $d$-dimensional vector space over a finite field with $q$ elements, $ {\Bbb F}_q^d$, contains a copy of every $k$-simplex. Fourier analytic methods, Kloosterman sums, and bootstrapping play an important role....
In this introduction we review the definition, a conjecture, and known resultson the restriction problem for algebraic varieties in d-dimensional vector spaces over finitefields. Let F dqbe a d-dimensional vector space over the finite field F q with q elements. Weendow this space with a ...
vector space n (Mathematics) maths a mathematical structure consisting of a set of objects (vectors) associated with a field of objects (scalars), such that the set constitutes an Abelian group and a further operation, scalar multiplication, is defined in which the product of a scalar and a...
vector spacefinite fieldThis paper is devoted to constructing an authentication code with arbitration using subspaces of vector spaces over finite fields. Moreover, if we choose the encoding rules of the transmitter and the decoding rules of the receiver according to a uniform probability distribution...
Ubiquity of simplices in subsets of vector spaces over finite fields We prove that a sufficiently large subset of the d-dimensional vector space over a finite field with q elements, $\\mathbb{F}$\\mathbb{F} q d , contains a ... HA Iosevich - 《Analysis Mathematica》 被引量: 70发表...
We only consider vector spaces over R. In this section, we construct an L vector space—a topological vector space that is an L space—whose square is neither normal nor weakly paracompact. A collection U of subsets of a space X is point finite if every x∈ X is in at most finitely...
A vector space, or sometimes linear space, V, over a field F, is an abelian group, written additively, with a map F× V→ V such that, for x,y∈V,α,β∈F, 1. αx+y=αx+αy (“linearity”), 2. α+βx=αx+βx, 3. (αβ)x = α(βx), and 4. 1x = x. A ve...
ON THE UNITARY INVARIANTS OF A SUBSPACE OF A VECTOR SPACE OVER A FINITE FIELD Let F q 2 be a finite field with q 2 elements, where q is a power of a prime and let a→a=a q (1) be the involutive automorphism of F q 2 with the fixe... Z Wan - 《Chinese Science Bulletin》...
The first three paragraphs are concerned with the elementary and purely algebraic properties of vector spaces E over a general commutative field. In § 7 the lattice V ( E ) of linear subspaces of E is studied, and § 8 deals with linear mappings from one vector space into another, and ...