7 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…
Quantitative Frameproof Codes and Hypergraphs
Wenjie Zhong, Xinqi Huang, Xiande Zhang
Frameproof codes are a class of secure codes introduced by Boneh and Shaw in the context of digital fingerprinting, and have been widely studied from a combinatorial point of view.…
Improved Bounds for Codes over Trees
Yanzhi Li, Wenjie Zhong, Tingting Chen +1
Codes over trees were introduced recently to bridge graph theory and coding theory with diverse applications in computer science and beyond. A central challenge lies in determining…
Improvements on Permutation Reconstruction from Minors
Yiming Ma, Wenjie Zhong, Xiande Zhang
We study the reconstruction problem of permutation sequences from their -minors, which are subsequences of length with entries renumbered by preserving order.…
Trace reconstruction of matrices and hypermatrices
Wenjie Zhong, Xiande Zhang
A \emph{trace} of a sequence is generated by deleting each bit of the sequence independently with a fixed probability. The well-studied \emph{trace reconstruction} problem asks how…
Reconstruction of hypermatrices from subhypermatrices
Xiande Zhang, Wenjie Zhong
For a given , what is the smallest number such that every sequence of length is determined by the multiset of all its -subsequences? This is called the -deck probl…