Gennian Ge

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research-article
Reconstruction From Noisy Substrings
- Hengjia Wei
  School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China
  ,
- Moshe Schwartz
  Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 70, Issue 11•Nov. 2024, pp 7757-7776 • https://doi.org/10.1109/TIT.2024.3454119
This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This coded ...
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Binary Codes for Correcting Two Edits
- Yubo Sun
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 70, Issue 10•Oct. 2024, pp 6877-6898 • https://doi.org/10.1109/TIT.2024.3445929
An edit refers to a single insertion, deletion, or substitution. This paper aims to construct binary codes that can correct two edits. To do this, a necessary and sufficient condition for a code to be two-edit correctable is provided, showing that a code ...
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Swap-Robust and Almost Supermagic Complete Graphs for Dynamical Distributed Storage
- Xin Wei
  School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China
  ,
- Xiande Zhang
  School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 70, Issue 8•Aug. 2024, pp 5606-5623 • https://doi.org/10.1109/TIT.2024.3404431
To prevent service time bottlenecks in distributed storage systems, the access balancing problem has been studied by designing almost supermagic edge labelings of certain graphs to balance the access requests to different servers. In this paper, we ...
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Constant L₁-Weight Codes Under L∞-Metric
- Tingting Chen
  Institute of Mathematics and Interdisciplinary Sciences, Xidian University, Xi’an, China
  ,
- Zhiwen He
  Zhejiang Lab, Hangzhou, China
  ,
- Gennian Ge
  School of Mathematics Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 70, Issue 7•July 2024, pp 4928-4945 • https://doi.org/10.1109/TIT.2024.3385419
This paper studies the construction of constant <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula>-weight codes under <inline-formula> <tex-math notation="LaTeX">$L_{\infty }$ </tex-math></inline-formula>-metric, which could ...
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A Rainbow Framework for Coded Caching and Its Applications
- Min Xu
  NITFID, LPMC, and KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin, China
  ,
- Zixiang Xu
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Min-Qian Liu
  NITFID, LPMC, and KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin, China
IEEE Transactions on Information Theory, Volume 70, Issue 3•March 2024, pp 1738-1752 • https://doi.org/10.1109/TIT.2024.3352020
The centralized coded caching focuses on reducing the network burden in peak times in a wireless network system. In this paper, motivated by the study of the only rainbow 3-term arithmetic progressions set, we propose a combinatorial framework for ...
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On linear diameter perfect Lee codes with distance 6
- Tao Zhang
  Zhejiang Lab, Hangzhou 311100, China
  ,
- Gennian Ge
  School of Mathematics Sciences, Capital Normal University, Beijing 100048, China
Journal of Combinatorial Theory Series A, Volume 201, Issue C•Jan 2024 • https://doi.org/10.1016/j.jcta.2023.105816
Abstract
In 1968, Golomb and Welch conjectured that there is no perfect Lee codes with radius r ≥ 2 and dimension n ≥ 3. A diameter perfect code is a natural generalization of the perfect code. In 2011, Etzion (2011) [5] proposed the following problem: ...
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On Lattice Tilings of ℤⁿ by Limited Magnitude Error Balls B(n, 2, 1, 1)
- Tao Zhang
  Zhejiang Laboratory, Hangzhou, China
  ,
- Yanlu Lian
  School of Mathematics, Hangzhou Normal University, Hangzhou, China
  ,
- Gennian Ge
  School of Mathematics Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 11•Nov. 2023, pp 7110-7121 • https://doi.org/10.1109/TIT.2023.3301669
Limited magnitude error model has applications in flash memory. In this model, a perfect code is equivalent to a tiling of <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}^{n}$ </tex-math></inline-formula> by limited magnitude error balls. In this ...
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Improved Gilbert-Varshamov Bounds for Hopping Cyclic Codes and Optical Orthogonal Codes
- Chenyang Zhang
  Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, China
  ,
- Chong Shangguan
  Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 11•Nov. 2023, pp 7099-7109 • https://doi.org/10.1109/TIT.2023.3296963
Hopping cyclic codes (HCCs) are (non-linear) cyclic codes with the additional property that the <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> cyclic shifts of every given codeword are all distinct, where <inline-formula> <...
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Robust Network Function Computation
- Hengjia Wei
  Peng Cheng Laboratory, Shenzhen, China
  ,
- Min Xu
  School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 11•Nov. 2023, pp 7070-7081 • https://doi.org/10.1109/TIT.2023.3296154
We consider the following robust computing problem in a directed acyclic network. A sink node is required to compute with zero error a target function of source messages which are generated at multiple source nodes, whereas the communication links might ...
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Some results on similar configurations in subsets of F q d
- Chengfei Xie
  School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Finite Fields and Their Applications, Volume 91, Issue C•Oct 2023 • https://doi.org/10.1016/j.ffa.2023.102252
Abstract
In this paper, we study problems about the similar configurations in F q d. Let G = ( V , E ) be a graph, where V = { 1 , 2 , … , n } and E ⊆ ( V 2 ). For a set E in F q d, we say that E contains a pair of G with dilation ratio r if ...
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Reconstruction of Sequences Distorted by Two Insertions
- Zuo Ye
  School of Mathematical Sciences, University of Science and Technology of China, Hefei, China
  ,
- Xin Liu
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Xiande Zhang
  School of Mathematical Sciences, University of Science and Technology of China, Hefei, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 8•Aug. 2023, pp 4977-4992 • https://doi.org/10.1109/TIT.2023.3260872
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 2001 and developed recently due to applications in modern storage devices ...
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Embedding bipartite distance graphs under Hamming metric in finite fields
- Zixiang Xu
  School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  ,
- Wenjun Yu
  School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Journal of Combinatorial Theory Series A, Volume 198, Issue C•Aug 2023 • https://doi.org/10.1016/j.jcta.2023.105765
Abstract
The famous Erdős-Falconer distance problems aim to quantify the extent to which large sets must determine many distinct distances. The problems in both the Euclidean setting and the discrete setting have received much attention. An ...
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Improved Constructions of Permutation and Multi-Permutation Codes Correcting a Burst of Stable Deletions
- Yubo Sun
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Yiwei Zhang
  Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, and the School of Cyber Science and Technology, Shandong University, Qingdao, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 7•July 2023, pp 4429-4441 • https://doi.org/10.1109/TIT.2023.3257174
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable deletions. In ...
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Sequence Reconstruction Under Single-Burst-Insertion/Deletion/Edit Channel
- Yubo Sun
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Yuanxiao Xi
  School of Mathematical Sciences, Zhejiang University, Hangzhou, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 7•July 2023, pp 4466-4483 • https://doi.org/10.1109/TIT.2023.3250459
Motivated by applications in modern storage devices such as DNA storage and racetrack memories, we study the sequence reconstruction problem which involves two important issues. One is determining the maximum intersection size between two error balls. The ...
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Covering Grassmannian Codes: Bounds and Constructions
- Bingchen Qian
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Xin Wang
  Department of Mathematics, Soochow University, Suzhou, China
  ,
- Chengfei Xie
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 6•June 2023, pp 3748-3758 • https://doi.org/10.1109/TIT.2023.3244939
Grassmannian <inline-formula> <tex-math notation="LaTeX">$\mathcal {G}_{q}(n,k)$ </tex-math></inline-formula> is the set of all <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-dimensional subspaces of the vector space <inline-...
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New lower bounds for the Turán density of PG _m(q)
- Tao Zhang
  Zhejiang Lab, Hangzhou 311100, China
  ,
- Gennian Ge
  School of Mathematics Sciences, Capital Normal University, Beijing 100048, China
Discrete Mathematics, Volume 346, Issue 6•Jun 2023 • https://doi.org/10.1016/j.disc.2023.113367
Abstract
Let H be an r-uniform hypergraph. The Turán number ex ( n , H ) is the maximum number of edges in an n-vertex H-free r-uniform hypergraph. The Turán density of H is defined by π ( H ) = lim n → ∞ ⁡ ex ( n , H ) ( n r ) . In this paper, we ...
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Improved Lower Bounds for Strongly Separable Matrices and Related Combinatorial Structures
- Bingchen Qian
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Xin Wang
  Department of Mathematics, Soochow University, Jiangsu, Suzhou, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 5•May 2023, pp 2801-2807 • https://doi.org/10.1109/TIT.2022.3233395
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> positive elements among <inline-formula> <tex-math ...
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Correcting Two-Deletion With a Constant Number of Reads
- Yubo Sun
  School of Mathematical Sciences, Capital Normal University, Beijing, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing, China
IEEE Transactions on Information Theory, Volume 69, Issue 5•May 2023, pp 2969-2982 • https://doi.org/10.1109/TIT.2022.3226296
Motivated by certain emerging storage media, such as DNA storage and racetrack memories, we study the problem of designing <inline-formula> <tex-math notation="LaTeX">$(n,N;\mathcal {D}_{k})$ </tex-math></inline-formula>-reconstruction codes, where the ...
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Coding schemes for locally balanced constraints
- Chen Wang
  Shandong University,Key Laboratory of Cryptologic Technology and Information Security of Ministry of Education, School of Cyber Science and Technology,Qingdao,China,266237
  ,
- Ziyang Lu
  Shandong University,Key Laboratory of Cryptologic Technology and Information Security of Ministry of Education, School of Cyber Science and Technology,Qingdao,China,266237
  ,
- Zhaojun Lan
  Capital Normal University,School of Mathematical Sciences,Beijing,China,100048
  ,
- Gennian Ge
  Capital Normal University,School of Mathematical Sciences,Beijing,China,100048
  ,
- Yiwei Zhang
  Shandong University,Key Laboratory of Cryptologic Technology and Information Security of Ministry of Education, School of Cyber Science and Technology,Qingdao,China,266237
2022 IEEE International Symposium on Information Theory (ISIT)•June 2022, pp 1342-1347• https://doi.org/10.1109/ISIT50566.2022.9834888
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the (ℓ, δ)-locally balanced constraint requires that the weight of any ...
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A note on multicolor Ramsey number of small odd cycles versus a large clique
- Zixiang Xu
  School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  ,
- Gennian Ge
  School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Discrete Mathematics, Volume 345, Issue 6•Jun 2022 • https://doi.org/10.1016/j.disc.2022.112823
Abstract
Let R k ( H ; K m ) be the smallest number N such that every coloring of the edges of K N with k + 1 colors has either a monochromatic H in color i for some 1 ⩽ i ⩽ k, or a monochromatic K m in color k + 1. In this short note, we study ...
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History: Disambiguation of author names is of course required for precise identification of all the works, and only those works, by a unique individual. Of equal importance to ACM, author name normalization is also one critical prerequisite to building accurate citation and download statistics. For the past several years, ACM has worked to normalize author names, expand reference capture, and gather detailed usage statistics, all intended to provide the community with a robust set of publication metrics. The Author Profile Pages reveal the first result of these efforts.
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ACM Author-Izer is a unique service that enables ACM authors to generate and post links on both their homepage and institutional repository for visitors to download the definitive version of their articles from the ACM Digital Library at no charge.

Downloads from these sites are captured in official ACM statistics, improving the accuracy of usage and impact measurements. Consistently linking to definitive version of ACM articles should reduce user confusion over article versioning.

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Sign in to your ACM web account and go to your Author Profile page. Click "Add personal information" and add photograph, homepage address, etc. Click ADD AUTHOR INFORMATION to submit change. Once you receive email notification that your changes were accepted, you may utilize ACM Author-izer.

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Sign in to your ACM web account, go to your Author Profile page in the Digital Library, look for the ACM Author-izer link below each ACM published article, and begin the authorization process. If you have published many ACM articles, you may find a batch Authorization process useful. It is labeled: "Export as: ACM Author-Izer Service"

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FAQ

Q. What is ACM Author-Izer?
A. ACM Author-Izer is a unique, link-based, self-archiving service that enables ACM authors to generate and post links on either their home page or institutional repository for visitors to download the definitive version of their articles for free.
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Q. Why should authors use ACM Author-Izer?
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Q. Does ACM Author-Izer provide benefits for authors?
A. Downloads of definitive articles via Author-Izer links on the authors’ personal web page are captured in official ACM statistics to more accurately reflect usage and impact measurements.

Authors who do not use ACM Author-Izer links will not have downloads from their local, personal bibliographies counted. They do, however, retain the existing right to post author-prepared preprint versions on their home pages or institutional repositories with DOI pointers to the definitive version permanently maintained in the ACM Digital Library.

Q. How does ACM Author-Izer benefit the computing community?
A. ACM Author-Izer expands the visibility and dissemination of the definitive version of ACM articles. It is based on ACM’s strong belief that the computing community should have the widest possible access to the definitive versions of scholarly literature. By linking authors’ personal bibliography with the ACM Digital Library, user confusion over article versioning should be reduced over time.

In making ACM Author-Izer a free service to both authors and visitors to their websites, ACM is emphasizing its continuing commitment to the interests of its authors and to the computing community in ways that are consistent with its existing subscription-based access model.

Q. How do authors access ACM Author-Izer?
A. See How to Use

Q. Why can’t I find my most recent publication in my ACM Author Profile Page?
A. There is a time delay between publication and the process which associates that publication with an Author Profile Page. Right now, that process usually takes 4-8 weeks.

Q. How does ACM Author-Izer expand ACM’s “Green Path” Access Policies?
A. ACM Author-Izer extends the rights and permissions that authors retain even after copyright transfer to ACM, which has been among the “greenest” publishers. ACM enables its author community to retain a wide range of rights related to copyright and reuse of materials. They include:
- Posting rights that ensure free access to their work outside the ACM Digital Library and print publications
- Rights to reuse any portion of their work in new works that they may create
- Copyright to artistic images in ACM’s graphics-oriented publications that authors may want to exploit in commercial contexts
- All patent rights, which remain with the original owner

Gennian Ge

Gennian Ge

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Results

Reconstruction From Noisy Substrings

Binary Codes for Correcting Two Edits

Swap-Robust and Almost Supermagic Complete Graphs for Dynamical Distributed Storage

Constant L₁-Weight Codes Under L∞-Metric

A Rainbow Framework for Coded Caching and Its Applications

On linear diameter perfect Lee codes with distance 6

On Lattice Tilings of ℤⁿ by Limited Magnitude Error Balls B(n, 2, 1, 1)

Improved Gilbert-Varshamov Bounds for Hopping Cyclic Codes and Optical Orthogonal Codes

Robust Network Function Computation

Some results on similar configurations in subsets of F q d

Reconstruction of Sequences Distorted by Two Insertions

Embedding bipartite distance graphs under Hamming metric in finite fields

Improved Constructions of Permutation and Multi-Permutation Codes Correcting a Burst of Stable Deletions

Sequence Reconstruction Under Single-Burst-Insertion/Deletion/Edit Channel

Covering Grassmannian Codes: Bounds and Constructions

New lower bounds for the Turán density of PG _m(q)

Improved Lower Bounds for Strongly Separable Matrices and Related Combinatorial Structures

Correcting Two-Deletion With a Constant Number of Reads

Coding schemes for locally balanced constraints

A note on multicolor Ramsey number of small odd cycles versus a large clique