The Tight Upper Bound for the Size of Single Deletion Error Correcting Codes in Dimension 11

TL;DR

This paper establishes the exact maximum size of single deletion error correcting codes in dimension 11, confirming the conjecture that the upper bound matches the VT code size for this case.

Contribution

The paper introduces an integer linear programming approach to determine the tight upper bound for SDECC size in dimension 11, extending previous results for dimensions up to 10.

Findings

The tight upper bound for SDECC in dimension 11 is 172.

The method confirms the conjecture for dimension 11.

Provides a computational approach for bounds in coding theory.

Abstract

A single deletion error correcting code (SDECC) is a set of fixed-length sequences consisting of two types of symbols, 0 and 1, such that the original sequence can be recovered for at most one deletion error. The upper bound for the size of SDECC is expected to be equal to the size of Varshamov-Tenengolts (VT) code, and this conjecture had been shown to be true when the code length is ten or less. In this paper, we discuss a method for calculating this upper bound by providing an integer linear programming solver with several linear constraints. As a new result, we obtained that the tight upper bound for the size of a single deletion error correcting code in dimension 11 is 172.