Singular matrices with restricted rows in vector spaces over finite fields

Distribution of Matrices with Restricted Entries over Finite Fields

For a prime p, we consider some natural classes of matrices over a finite field Fp of p elements, such as matrices of given rank or with characteristic polynomial having irreducible divisors of prescribed degrees. We demonstrate two different techniques which allow us to show that the number of such matrices in each of these classes and also with components in a given subinterval [−H,H] ⊆ [−(p ...

New Construction of Deterministic Compressed Sensing Matrices via Singular Linear Spaces over Finite Fields

As an emerging approach of signal processing, not only has compressed sensing (CS) successfully compressed and sampled signals with few measurements, but also has owned the capabilities of ensuring the exact recovery of signals. However, the above-mentioned properties are based on the (compressed) sensing matrices. Hence the construction of sensing matrices is the key problem. Compared with the...

Extension and averaging operators in vector spaces over finite fields

We study the mapping properties of both extension operators and averaging operators associated with the algebraic variety S = {x ∈ Fq : Q(x) = 0} where Q(x) is a nondegenerate quadratic form over the finite field Fq. Carbery, Stones, and Wright [3] established a method to deduce L − L estimates for averaging operators over a general variety. As a core result in this paper, we give the sharp est...

Extension Theorems in Vector Spaces over Finite Fields

Orthogonal Systems in Vector Spaces over Finite Fields

We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.