A class of quantum synchronizable codes of length $2^n$ over ${\rm F}_q$

TL;DR

This paper introduces a new class of quantum synchronizable codes of length 2^n that utilize cyclotomic cosets, achieving optimal synchronization correction capabilities up to the theoretical maximum.

Contribution

The paper constructs a novel class of quantum synchronizable codes of length 2^n using cyclotomic cosets, with synchronization capabilities reaching the upper bound.

Findings

Codes achieve maximum synchronization correction of 2^n

Construction method based on cyclotomic cosets

Enhances quantum error correction and synchronization

Abstract

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes which can be used to correct the effects of quantum noise on qubits and misalignment in block synchronization. In this paper, a new class of quantum synchronizable codes of length $2^n$ are constructed by using the cyclotomic cosets, whose synchronization capabilities always reach the upper bound $2^n$.