Constructive Conjugate Codes for Quantum Error Correction and Cryptography

TL;DR

This paper introduces a polynomial construction method for conjugate code pairs, which are fundamental to quantum error correction and cryptography, achieving high rates and efficient decoding algorithms.

Contribution

It presents a novel polynomial construction of conjugate code pairs that attain the highest known rates and are decodable with polynomial complexity.

Findings

Achieves highest known rates on additive channels

Provides polynomial-time decoding algorithms

Enhances quantum error correction and cryptography applications

Abstract

A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum error-correcting code. It is known that conjugate code pairs are applicable to quantum cryptography. In this work, a polynomial construction of conjugate code pairs is presented. The constructed pairs achieve the highest known achievable rate on additive channels, and are decodable with algorithms of polynomial complexity.