A basic problem for the constant dimension subspace coding is to determine the maximal possible size Aq(n; d; k) of a set of k-dimensional subspaces in Fn q such that the subspace distance satisfies d(U; V ) = 2k – 2 dim(U V) ≥ d for any two different subspaces U and V in this set. We present two new constructions of constant dimension subspace codes using subsets of maximum rank-distance (MRD) codes in several blocks. This method is firstly applied to the linkage construction and secondly to arbitrary number of blocks of lifting MRD codes. In these two constructions, subsets of MRD codes with bounded ranks play an essential role. The Delsarte theorem about the rank distribution of MRD codes is an important ingredient to count codewords in our constructed constant dimension subspace codes. We give many new lower bounds for Aq(n; d; k). More than 110 new constant dimension subspace codes better than previously best known codes are constructed.

The linkage construction and its generalization is one of the most powerful constructions for constant dimension codes, accounting for approximately 50% of all the listed parameters. We show how to improve the linkage construction of subspace codes by two parallel versions of the linkage construction. This proof allows us to attain codes of larger size for a given minimum distance, which exceeds the latest improvements on the linkage construction [2] in the cases Aq(13; 4, 4),Aq(17, 4, 4), and Aq(19, 6, 6).

Echelon-Ferrers is an important method to improve lower bounds for constant-dimension codes, which can be applied on various parameters. Fagang Li [12] combined the linkage construction and echelon-Ferrers to obtain some new lower bounds of constant-dimension codes. In this letter, we generalize this linkage construction to obtain new lower bounds.

With its potential to solve the problem of car parking difficulties, smart parking management systems have elicited a significant amount of interest from both academia and industry. Robust and reliable parking detection is a key technology for smart parking management systems. Presently, magnetic sensors are being widely used in parking detection. However, they are prone to produce high false and missed detection rates in environments that have geomagnetic interference. This article proposes a new sensing device based on the combination of a magnetic sensor and a pulsed coherent radar. The sensing device is used for parking detection in the context of Internet of Things. A Dempster–Shafer evidence theory-based collaborative fusion approach is developed to improve the accuracy of vehicle detection. Pulsed coherent radar is triggered by the magnetic sensor to reduce sampling power consumption. The prototype system is tested under various interference conditions. The results show that the combination of magnetic and radar sensors improves vehicle detection accuracy, and the lifetime of battery-powered sensor node is longer than five years.

One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\mathbf{A}}_{q}(n,d,k)$ of a set of $k$ -dimensional subspaces in $\mathbb F_{q}^{n}$ such that the subspace distance satisfies $\text {d}_{\text {S}}(U,V) = \dim (U+V)-\dim (U\cap V)\,\,\geq d$ for any two different $k$ -dimensional subspaces $U$ and $V$ in this set. In this letter, we propose a construction for constant dimension subspace codes by inserting a composite structure composing of an MRD code and its sub-codes. Its vast advantage over the previous constructions has been confirmed through extensive examples. At least 49 new constant dimension subspace codes which exceeds the currently best codes are constructed.