12 papers · 1 filter
Dot-product graphs in finite fields
Chengfei Xie, Gennian Ge
In this paper, we study the dot-product graphs in . We prove that if the size of the product of two adjacent sets is large enough, then the set of dot-product graph…
Reconstruction Codes for Deletions and Insertions: Connection, Distinction, and Construction
Yubo Sun, Gennian Ge
Let be an error ball function. A set of -ary sequences of length is referred to as an \emph{-reconstruction code} if each sequence…
On the Existence and Nonexistence of Splitter Sets
Zhiyu Yuan, Rongquan Feng, Gennian Ge
In this paper, the existence of perfect and quasi-perfect splitter sets in finite abelian groups is studied, motivated by their application in coding theory for flash memory storag…
On the Maximum Size of Codes Under the Damerau-Levenshtein Metric
Zuo Ye, Gennian Ge
The Damerau-Levenshtein distance between two sequences is the minimum number of operations (deletions, insertions, substitutions, and adjacent transpositions) required to convert o…
Correcting Bursty/Localized Deletions: A New Error-Position-Estimation Code
Zuo Ye, Yubo Sun, Gennian Ge
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with m…
Optimal Reconstruction Codes with Given Reads in Multiple Burst-Substitutions Channels
Wenjun Yu, Yubo Sun, Zixiang Xu +2
We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the…
On the Fixed-Length-Burst Levenshtein Ball with Unit Radius
Yuanxiao Xi, Yubo Sun, Gennian Ge
Consider a length- sequence over a -ary alphabet. The \emph{fixed-length Levenshtein ball} of radius encompasses all length- -ary s…
Correcting Errors Through Partitioning and Burst-Deletion Correction
Yubo Sun, Gennian Ge
In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlapping -deletion -substitution balls into sub-pairs, where the -bur…
Criss-Cross Deletion Correcting Codes: Optimal Constructions with Efficient Decoders
Yubo Sun, Gennian Ge
This paper addresses fundamental challenges in two-dimensional error correction by constructing optimal codes for \emph{criss-cross deletions}. We consider an array…
New Wide Locally Recoverable Codes with Unified Locality
Liangliang Xu, Fengming Tang, Tingting Chen +3
Wide Locally Recoverable Codes (LRCs) have recently been proposed as a solution for achieving high reliability, good performance, and ultra-low storage cost in distributed storage…
Binary Reconstruction Codes for Correcting One Deletion and One Substitution
Yuling Li, Yubo Sun, Gennian Ge
In this paper, we investigate binary reconstruction codes capable of correcting one deletion and one substitution. We define the \emph{single-deletion single-substitution ball} fun…
Sequence Reconstruction under Channels with Multiple Bursts of Insertions or Deletions
Zhaojun Lan, Yubo Sun, Wenjun Yu +1
The sequence reconstruction problem involves a model where a sequence is transmitted over several identical channels. This model investigates the minimum number of channels require…