Constructive Conjugate Codes for Quantum Error Correction and Cryptography
arXiv:cs/0703141
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.
10 pages, 1 figure. Ver.2: statement in Theorem 7.1 was revised to a more general one, which the proof (unchanged except a couple of lines after Eq.(11)) had really implied. A corollary to this theorem was added. Annotative parts on achievable rates (mainly after the proof of Theorem 7.1) were revised