TU2.R6.3

Improving the Singleton-type Upper Bounds for Non-Linear Deletion Correcting Codes

Shiqin Liu, Chen Wang, Shandong University, China; Gennian Ge, Capital Normal University, China; Yiwei Zhang, Shandong University, China

Session:
Biology: Insertions and Deletions

Track:
17: Information and Coding in Biology

Location:
Sigma/Delta

Presentation Time:
Tue, 9 Jul, 12:10 - 12:30

Session Chair:
Maël Le Treust, CNRS
Abstract
Codes correcting insertion and deletion errors have received considerable attention in recent years due to their applications in DNA storage and other communication and storage systems with synchronization errors. Given two sequences $\boldsymbol{u}$ and $\boldsymbol{v}$, their insdel (short for insertion and deletion) distance is defined as the minimum number of insertions and deletions needed to transform one sequence into the other. Let $I_q(n,d)$ be the maximum size of a code $\mathcal{C}\subseteq \Sigma^n$ where $|\Sigma|=q$, such that any two distinct codewords have insdel distance at least $d$. In this paper, we analyze the upper bound of $I_q(n,d)$ and improve the results from Liu and Xing [IEEE-IT. 69(2), 928-940, 2023].
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