Xiande Zhang

activity

20102026

most citedStrongly nonlocal unextendible product bases do exist

40 citations · 112 across the 31 of their papers we have counts for

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13 papers · 1 filter

math.CO2026

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 $e$ -perfect codes in the Johnson…

math.CO2026

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…

math.CO2023★ 1 cited

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 $A$ of subsets of an $n$ element set, let $o p (A)$ denote the number of distinct pair…

math.CO2020

Optimal Ternary Codes with Weight $w$ and Distance $2 w - 2$ in $ℓ_{1}$ -Metric

Xin Wei, Tingting Chen, Xiande Zhang

The study of constant-weight codes in $ℓ_{1}$ -metric was motivated by the duplication-correcting problem for data storage in live DNA. It is interesting to determine the maximum s…

math.CO2019★ 1 cited

Bollobás type theorems for hemi-bundled two families

Wenjun Yu, Xiangliang Kong, Yuanxiao Xi +2

Let ${(A_{i}, B_{i})}_{i = 1}^{m}$ be a collection of pairs of sets with $∣ A_{i} ∣ = a$ and $∣ B_{i} ∣ = b$ for $1 \leq i \leq m$ . Suppose that $A_{i} \cap B_{j} = \emptyset$ if and only if $i = j$ , then by…

math.CO2019

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,…

math.CO2019

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 $l_{\infty}$ -metric. We determine the covering radius of the $(p, q)$ -type group, which is a direct pro…

math.CO2018

Suitable sets of permutations, packings of triples, and Ramsey's theorem

Xiande Zhang

A set of $N$ permutations of ${1, 2, \dots, v}$ is $t$ -suitable, if each symbol precedes each subset of $t - 1$ others in at least one permutation. The extremal problem of determinin…

math.CO2015

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 $n$ , distance $d = 2 w - 1$ and constant composition $w$ is $⌊ \frac{n}{w _{1}} ⌋$ , where $w$ i…

math.CO2014★ 5 cited

Decompositions of Edge-Colored Digraphs: A New Technique in the Construction of Constant-Weight Codes and Related Families

Yeow Meng Chee, Fei Gao, Han Mao Kiah +3

We demonstrate that certain Johnson-type bounds are asymptotically exact for a variety of classes of codes, namely, constant-composition codes, nonbinary constant-weight codes and…

math.CO2012

On the Existence of Retransmission Permutation Arrays

Ian M. Wanless, Xiande Zhang

We investigate retransmission permutation arrays (RPAs) that are motivated by applications in overlapping channel transmissions. An RPA is an $n \times n$ array in which each row is…

math.CO2012

Improved Constructions of Frameproof Codes