20 citations · 30 across the 11 of their papers we have counts for
16 papers
Random Gabidulin Codes Achieve List Decoding Capacity in the Rank Metric
Zeyu Guo, Chaoping Xing, Chen Yuan +1
Gabidulin codes, serving as the rank-metric counterpart of Reed-Solomon codes, constitute an important class of maximum rank distance (MRD) codes. However, unlike the fruitful posi…
Constructions of -uniform states in heterogeneous systems
Keqin Feng, Lingfei Jin, Chaoping Xing +1
A pure quantum state of parties associated with the Hilbert space $\CC^{d_1}\otimes \CC^{d_2}\otimes\cdots\otimes \CC^{d_n}$ is called -uniform if all the reductions to -…
On the Fine-Grained Complexity of Small-Size Geometric Set Cover and Discrete -Center for Small
Timothy M. Chan, Qizheng He, Yuancheng Yu
We study the time complexity of the discrete -center problem and related (exact) geometric set cover problems when or the size of the cover is small. We obtain a plethora of…
Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery
Nicolas Resch, Chen Yuan, Yihan Zhang
In this work we consider the list-decodability and list-recoverability of arbitrary -ary codes, for all integer values of . A code is called -list-decodable if…
Upper bounds on maximum lengths of Singleton-optimal locally repairable codes
Shu Liu, Tingyi Wu, Chaoping Xing +1
A locally repairable code is called Singleton-optimal if it achieves the Singleton-type bound. Such codes are of great theoretic interest in the study of locally repairable codes.…
Threshold Rates of Codes Ensembles: Linear is Best
Nicolas Resch, Chen Yuan
In this work, we prove new results concerning the combinatorial properties of random linear codes. Firstly, we prove a lower bound on the list-size required for random linear codes…
Beating the probabilistic lower bound on -perfect hashing
Chaoping Xing, Chen Yuan
For an integer , a perfect -hash code is a block code over of length in which every subset $\{\mathbf{c}_1,\mathbf{c}_2,\dots,\mathbf{c}_q\…
Construction of optimal locally recoverable codes and connection with hypergraph
Chaoping Xing, Chen Yuan
Recently, it was discovered by several authors that a -ary optimal locally recoverable code, i.e., a locally recoverable code archiving the Singleton-type bound, can have length…
Asymptotic Gilbert-Varshamov bound on Frequency Hopping Sequences
Xianhua Niu, Chaoping Xing, Chen Yuan
Given a -ary frequency hopping sequence set of length and size with Hamming correlation , one can obtain a -ary (nonlinear) cyclic code of length and size …
How long can optimal locally repairable codes be?
Venkatesan Guruswami, Chaoping Xing, Chen Yuan
A locally repairable code (LRC) with locality allows for the recovery of any erased codeword symbol using only other codeword symbols. A Singleton-type bound dictates the b…
List Decodability of Symbol-Pair Codes
Shu Liu, Chaoping Xing, Chen Yuan
We investigate the list decodability of symbol-pair codes in the present paper. Firstly, we show that list decodability of every symbol-pair code does not exceed the Gilbert-Varsha…
Optimal locally repairable codes of distance and via cyclic codes
Yuan Luo, Chaoping Xing, Chen Yuan
Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code {\it optimal} if it achieves the Singleton-type bound).…
Subspace Designs based on Algebraic Function Fields
Venkatesan Guruswami, Chaoping Xing, Chen Yuan
Subspace designs are a (large) collection of high-dimensional subspaces of $\F_q^m$ such that for any low-dimensional subspace , only a small number of subspaces from…
Efficient Multi-Point Local Decoding of Reed-Muller Codes via Interleaved Codex
Ronald Cramer, Chaoping Xing, Chen Yuan
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves…
Multipartite entangled states, symmetric matrices and error-correcting codes
Keqin Feng, Lingfei Jin, Chaoping Xing +1
A pure quantum state is called -uniform if all its reductions to -qudit are maximally mixed. We investigate the general constructions of -uniform pure quantum states of $n…
A new class of rank-metric codes and their list decoding beyond the unique decoding radius
Chaoping Xing, Chen Yuan
Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. Although the list decodability of random rank-metric codes and limits to lis…