40 citations · 112 across the 31 of their papers we have counts for
31 papers
The Last Seven Open Radii for Perfect Codes in the Johnson Scheme
Xiande Zhang, Wenjie Zhong
Delsarte (1973) conjectured that there are no nontrivial perfect codes in the Johnson scheme. In this paper, we prove that there are no nontrivial -perfect codes in the Johnson…
There Are No Nontrivial Perfect Codes in the Johnson Scheme
Tuvi Etzion, Xiande Zhang, Wenjie Zhong
In his seminal work from 1973, Delsarte conjectured that the Johnson schemes admit no nontrivial perfect codes. We prove this fundamental conjecture which is central in combinatori…
Unextendible product bases from orthogonality graphs
Fei Shi, Ge Bai, Xiande Zhang +2
Unextendible product bases (UPBs) play a key role in the study of quantum entanglement and nonlocality. A famous open question is whether there exist genuinely unextendible product…
Reconstruction of Sequences Distorted by Two Insertions
Zuo Ye, Xin Liu, Xiande Zhang +1
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in…
On supersaturation for oddtown and eventown
Xin Wei, Yuhao Zhao, Xiande Zhang +1
We study the supersaturation problems of oddtown and eventown. Given a family of subsets of an element set, let denote the number of distinct pair…
Unextendible and uncompletable product bases in every bipartition
Fei Shi, Mao-Sheng Li, Xiande Zhang +1
Unextendible product basis is an important object in quantum information theory and features a broad spectrum of applications, ranging bound entangled states, quantum nonlocality w…
Balanced reconstruction codes for single edits
Rongsheng Wu, Xiande Zhang
Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai \emph{et al}. to combat errors when a fixed number of noisy c…
Strong quantum nonlocality and unextendibility without entanglement in -partite systems with odd
Yiyun He, Fei Shi, Xiande Zhang
A set of orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entangle…
Strong quantum nonlocality for unextendible product bases in heterogeneous systems
Fei Shi, Mao-Sheng Li, Lin Chen +1
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality wit…
Unextendible product operator basis
Mengyao Hu, Lin Chen, Fei Shi +2
Quantum nonlocality is associated with the local indistinguishability of orthogonal states. Unextendible product basis (UPB), a widely used tool in quantum information, exhibits no…
Strongly nonlocal unextendible product bases do exist
Fei Shi, Mao-Sheng Li, Mengyao Hu +4
A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measure…
Sparse and Balanced MDS Codes over Small Fields
Tingting Chen, Xiande Zhang
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load.…
Optimal Ternary Codes with Weight and Distance in -Metric
Xin Wei, Tingting Chen, Xiande Zhang
The study of constant-weight codes in -metric was motivated by the duplication-correcting problem for data storage in live DNA. It is interesting to determine the maximum s…
Optimal codes with small constant weight in -metric
Tingting Chen, Yiming Ma, Xiande Zhang
Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in -metric. By using packings and group div…
Optimal Fraction Repetition Codes for Access-Balancing in Distributed Storage
Wenjun Yu, Xiande Zhang, Gennian Ge
To solve the access-balancing problem in distributed storage systems, we introduce a new combinatorial model, called MinVar model for fractional repetition (FR) codes. Since FR cod…
Some New Results on Splitter Sets
Zuo Ye, Tao Zhang, Xiande Zhang +1
Splitter sets have been widely studied due to their applications in flash memories, and their close relations with lattice tilings and conflict avoiding codes. In this paper, we gi…
Bollobás type theorems for hemi-bundled two families
Wenjun Yu, Xiangliang Kong, Yuanxiao Xi +2
Let be a collection of pairs of sets with and for . Suppose that if and only if , then by…
Repairing Generalized Reed-Muller Codes
Tingting Chen, Xiande Zhang
In distributed storage systems, both the repair bandwidth and locality are important repair cost metrics to evaluate the performance of a storage code. Recently, Guruswami and Woot…
Complexity of Dependencies in Bounded Domains, Armstrong Codes, and Generalizations
Yeow Meng Chee, Hui Zhang, Xiande Zhang
The study of Armstrong codes is motivated by the problem of understanding complexities of dependencies in relational database systems, where attributes have bounded domains. A $(q,…
Optimal -Ary Error Correcting/All Unidirectional Error Detecting Codes
Yeow Meng Chee, Xiande Zhang
Codes that can correct up to symmetric errors and detect all unidirectional errors, known as -EC-AUED codes, are studied in this paper. Given positive integers , and…
Covering Radius of Permutation Groups with Infinity-Norm
Xin Wei, Xiande Zhang
The covering radius of permutation group codes are studied in this paper with -metric. We determine the covering radius of the -type group, which is a direct pro…
Suitable sets of permutations, packings of triples, and Ramsey's theorem
Xiande Zhang
A set of permutations of is -suitable, if each symbol precedes each subset of others in at least one permutation. The extremal problem of determinin…
On the List-Decodability of Random Self-Orthogonal Codes
Lingfei Jin, Chaoping Xing, Xiande Zhang
In 2011, Guruswami-Håstad-Kopparty \cite{Gru} showed that the list-decodability of random linear codes is as good as that of general random codes. In the present paper, we further…
Linear Size Constant-Composition Codes Meeting the Johnson Bound
Yeow Meng Chee, Xiande Zhang
The Johnson-type upper bound on the maximum size of a code of length , distance and constant composition is , where i…