Deletion-correcting codes and dominant vectors

TL;DR

This paper characterizes pairs of binary vectors with subset deletion properties for t=1,2, aiding in understanding the maximum size of binary deletion-correcting codes.

Contribution

It provides a complete description of vector pairs with subset deletion properties for t=1,2, advancing the analysis of deletion-correcting code bounds.

Findings

Characterization of all such vector pairs for t=1,2

Insights into the structure of deletion-correcting codes

Implications for calculating L_2(n,t)

Abstract

In this paper we describe all pairs of binary vectors $({\bf u}, {\bf v})$ such that the set of vectors obtained by $t$ deletions in ${\bf v}$ is a subset of the set of vectors obtained by $t$ deletions in ${\bf u}$ for $t=1,2$. Such pairs play an important role for finding the value of $L_2(n,t)$, the maximum cardinality of binary $t$-deletion-correcting code of length $n$.