Conjugate Codes for Secure and Reliable Information Transmission

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 code. It is known that conjugate code pairs are applicable to (quantum) cryptography. In this work, polynomially constructible and efficiently decodable conjugate code pairs are presented. The constructed pairs achieve the highest known achievable rate on additive channels.