Gennian Ge

Substring Edit Correcting Codes and Optimal Single Burst-Deletion Correcting Codes

Zuo Ye, Gennian Ge

A $k$ -substring edit in a sequence first deletes a substring of length at most $k$ , and then inserts a sequence of length at most $k$ at the same position. A code that can correct…

Polynomially Improved Lower Bounds for Trifferent Codes via Locally Sparse $3$ -Uniform Hypergraphs

Xuejiao Han, Yubo Sun, Gennian Ge

A ternary code is \emph{trifferent} if every three distinct codewords have a coordinate in which their symbols are pairwise distinct. Let $T (n)$ be the maximum size of a trifferent…

New Results on Limited Magnitude Error Correcting Codes

Zhiyu Yuan, Tingting Chen, Rongquan Feng +1

This paper investigates the existence, construction and classification of limited magnitude error-correcting codes, with a focus on splitter sets and their connections to group spl…

Bounds and Constructions of Codes for Ordered Composite DNA Sequences

Zuo Ye, Yuling Li, Zhaojun Lan +1

This paper extends the foundational work of Dollma \emph{et al}. on codes for ordered composite DNA sequences. We consider the general setting with an alphabet of size $q$ and a re…

On the Palindromic/Reverse-Complement Duplication Correcting Codes

Yubo Sun, Gennian Ge

Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and co…

math.CO2025

Dot-product graphs in finite fields

Chengfei Xie, Gennian Ge

In this paper, we study the dot-product graphs in $F_{q}^{d}$ . 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 $B (\cdot)$ be an error ball function. A set of $q$ -ary sequences of length $n$ is referred to as an \emph{ $(n, q, N; B)$ -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- $n$ sequence $x$ over a $q$ -ary alphabet. The \emph{fixed-length Levenshtein ball} $L_{t} (x)$ of radius $t$ encompasses all length- $n$ $q$ -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 $t$ -deletion $s$ -substitution balls into sub-pairs, where the $^{\leq} t$ -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 $n \times n$ array…

cs.DC2025

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…

Constrained coding upper bounds via Goulden-Jackson cluster theorem

Yuanting Shen, Chong Shangguan, Zhicong Lin +1

Motivated by applications in DNA-based data storage, constrained codes have attracted a considerable amount of attention from both academia and industry. We study the maximum cardi…

Bounds and Constructions of $ℓ$ -Read Codes under the Hamming Metric

Yubo Sun, Gennian Ge

Nanopore sequencing is a promising technology for DNA sequencing. In this paper, we investigate a specific model of the nanopore sequencer, which takes a $q$ -ary sequence of length…

Binary Codes for Correcting Two Edits

Yubo Sun, Gennian Ge

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 condit…