Work

On the Size of Balls and Anticodes of Small Diameter Under the Fixed-Length Levenshtein Metric

Year: 2022

Type: article

Abstract: The rapid development of DNA storage has brought the deletion and insertion channel to the front line of research. When the number of deletions is equal to the number of insertions, theFixed Length Levenshtein(FLL) metric is the right measure for the distance between two words of the same length. Similar to any other metric, the size of a ball is one of the most fundamental parameters. In this work, we consider the minimum, maximum, and average size of a ball with radius one, in the FLL metric. The related minimum and the maximum size of a maximal anticode with diameter one are also considered.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2022.3227128

Authors: Daniella Bar-Lev, Tuvi Etzion, Eitan Yaakobi

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Israel Science Foundation

Award: G2848719540