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Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
Publicly available collections of drug-like molecules have grown to comprise 10s of billions of possibilities in recent history due to advances in chemical synthesis. Traditional methods for identifying "hit" molecules from a large…
Recently, two-dimensional (2D) array codes have been found to have applications in wireless communication.In this paper, we propose direct construction of 2D complete complementary codes (2D-CCCs) with arbitrary array size and flexible set…
In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear…
In this paper, we propose locally repairable codes (LRCs) with optimal minimum distance for distributed storage systems (DSS). A two-layer encoding structure is employed to ensure data reconstruction and the designated repair locality. The…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
Optimal rank-metric codes in Ferrers diagrams can be used to construct good subspace codes. Such codes consist of matrices having zeros at certain fixed positions. This paper generalizes the known constructions for Ferrers diagram…
Researchers in the biological sciences nowadays often encounter the curse of high-dimensionality, which many previously developed statistical models fail to overcome. To tackle this problem, sufficient dimension reduction aims to estimate…
Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant…
The coding problem considered in this work is to construct a linear code $\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary vector $\mathbf{r} \in \mathbb{F}^{n}$ is contained in the code. We study a recent…
Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The constructed…
A new construction for constant weight codes is presented. The codes are constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These subspaces form a constant dimension code in the Grassmannian space $\cG_q(n,k)$. Some of…
Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multi-level space-time codes for flat fading channels have been designed from sets…
We introduce a reversible deep learning model for 13C NMR that uses a single conditional invertible neural network for both directions between molecular structures and spectra. The network is built from i-RevNet style bijective blocks, so…
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…
An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between $\Delta$-complexes is a $\Delta$-map that induces injections from star sets of $\mathcal D$ to star sets of $\mathcal C$. We study immersions between finite-dimensional…
Spatially-coupled (SC) codes are constructed by coupling many regular low-density parity-check codes in a chain. The decoding chain of SC codes stops when facing burst erasures. This problem can not be overcome by increasing coupling…
Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…
We present the first theoretical framework that connects predictive coding (PC), a biologically inspired local learning rule, with the minimum description length (MDL) principle in deep networks. We prove that layerwise PC performs…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of LDPC codes with a simple construction facilitating hardware implementation while achieving excellent performance. In this paper, we introduce an algorithm that…