Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some Sidon spaces by using primitive elements and the roots of some irreducible polynomials over finite fields. Let q be a prime power, k, m, n be three positive integers and $ ho= lceil rac{m}{2k} ceil-1$, $ heta= lceil rac{n}{2m} ceil-1$. Based on these Sidon spaces and the union of some Sidon spaces, new cyclic subspace codes with size $rac{3(q^{n}-1)}{q-1}$ and $rac{ heta ho q^{k}(q^{n}-1)}{q-1}$ are obtained. The size of these codes is lager compared to the known constructions from [14] and [10].

In this letter, as a generalization of Heng's constructions in the paper [9], a construction of codebooks, which meets the Welch bound asymptotically, is proposed. The parameters of codebooks presented in this paper are new in some cases.

In this letter, as a generalization of Luo et al.'s constructions, a construction of codebook, which meets the Welch bound asymptotically, is proposed. The parameters of codebook presented in this paper are new in some cases.

In this letter, motivated by the research of Tian et al., two constructions of asymptotically optimal codebooks in regard to the Welch bound with additive and multiplicative characters are provided. The parameters of constructed codebooks are new, which are different from those in the letter of Tian et al.

Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that a sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a main problem in compressed sensing theory (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than k on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.