相关论文: An Explicit, Coupled-Layer Construction of a High-…
Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed…
We analyze permutation routing of rigid blocks representing surface code patches of $d_C^2$ atoms on a reconfigurable lattice with hypergraph transformations. For a hypergraph $H$, code distance $d_C$, $s=d_C^2$, number of blocks $N_L$, and…
Quantum computing requires effective error correction strategies to mitigate noise and decoherence. Quantum Low-Density Parity-Check (QLDPC) codes have emerged as a promising solution for scalable Quantum Error Correction (QEC) applications…
In this paper distributed storage systems with exact repair are studied. A construction for regenerating codes between the minimum storage regenerating (MSR) and the minimum bandwidth regenerating (MBR) points is given. To the best of…
We provide a recipe to construct towers of fields producing high order elements in $\mathrm{GF}(q,2^n)$, for odd $q$, and in $\mathrm{GF}(2,2 \cdot 3^n)$, for $n \ge 1$. These towers are obtained recursively by $x_{n}^2 + x_{n} = v(x_{n -…
Recently, subfield codes of geometric codes over large finite fields $\gf(q)$ with dimension $3$ and $4$ were studied and distance-optimal subfield codes over $\gf(p)$ were obtained, where $q=p^m$. The key idea for obtaining very good…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
We propose a new family of spatially coupled product codes, called sub-block rearranged staircase (SR-staircase) codes. Each SR-staircase code block is constructed by encoding rearranged preceding code blocks and new information blocks,…
A Quasi-Orthogonal Space-Time Block Code (QO-STBC) is attractive because it achieves higher code rate than Orthogonal STBC and lower decoding complexity than nonorthogonal STBC. In this paper, we first derive the algebraic structure of…
We consider the coarse-graining of holographic quantum error correcting codes under a generalized notion of bulk renormalization-group flow. In particular, we study the renormalization under this flow of the $A/4G$ term in the…
A (q,k,t)-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most q non-zeros, each column has at least k non-zeros and the supports of every two columns…
A $k$-deck of a (coloured) graph is a multiset of its induced $k$-vertex subgraphs. Given a graph $G$, when is it possible to reconstruct with high probability a uniformly random colouring of its vertices in $r$ colours from its $k$-deck?…
A linear code of length $n$ over a finite chain ring $R$ with residue field $\F_q$ is a $R$-submodule of $R^n$. A $R$-linear code is a code over $\F_q$ (not necessarily linear) which is the generalized Gray map image of a linear code over…
Quantum repeater is the key technology enabler for long-distance quantum communication. To date, most of the existing quantum repeater protocols are designed based on specific quantum codes or graph states. In this paper, we propose a…
Natural question generation (QG) aims to generate questions from a passage and an answer. Previous works on QG either (i) ignore the rich structure information hidden in text, (ii) solely rely on cross-entropy loss that leads to issues like…
We study exact-regenerating codes for entanglement-assisted distributed storage systems. Consider an $(n,k,d,\alpha,\beta_{\mathsf{q}},B)$ distributed system that stores a file of $B$ classical symbols across $n$ nodes with each node…
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…
We show that quantum Reed-Solomon codes constructed from classical Reed-Solomon codes can approach the capacity on the quantum erasure channel of $d$-level systems for large dimension $d$. We study the performance of one-way quantum…
The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…
This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an…