Connectivity of Synchronizable Codes in the N-Cube

Abstract

A binary code has bounded synchronization delay if there exists an integer $s$ such that at most $s$ consecutive bits are required to establish word synchronization in any message. The code whose words are lexicographically least in the non-periodic orbits determined by cyclic permutation of all words of length $n$ is called the canonical bounded synchronization delay code. It has the maximal number of words possible in a synchronizable code of fixed word length. Any code of fixed word length $n$ can be represented as a set of vertices in the $n$-cube. We prove that the canonical bounded synchronization delay code is a connected subset of the $n$-cube.