17 papers
Polynomially Improved Lower Bounds for Trifferent Codes via Locally Sparse -Uniform Hypergraphs
Xuejiao Han, Yubo Sun, Gennian Ge
The paper improves the known lower bound on the size of ternary trifferent codes by a factor of √n, using a refined concatenation method that employs locally sparse 3‑uniform hyper…
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 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 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…
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…