13 papers
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 is the insertion of the reversed and co…
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…