Zero-knowledge codes, introduced by Decatur, Goldreich, and Ron (ePrint 1997), are error-correcting codes in which few codeword symbols reveal no information about the encoded message, and have been extensively used in cryptographic constructions. Quantum CSS codes, introduced by Calderbank and Shor (Phys. Rev. A 1996) and Steane (Royal Society A 1996), are error-correcting codes that allow for quantum error correction, and are also useful for applications in quantum complexity theory. In this short note, we show that (linear, perfect) zero-knowledge codes and quantum CSS codes are equivalent. We demonstrate the potential of this equivalence by using it to obtain explicit asymptotically-good zero-knowledge locally-testable codes.

翻译：零知识编码由Decatur、Goldreich与Ron（ePrint 1997）提出，是一种纠错编码，其特点是少量码字符号不会泄露任何关于编码消息的信息，该编码已在密码学构造中得到广泛应用。量子CSS码由Calderbank与Shor（Phys. Rev. A 1996）以及Steane（Royal Society A 1996）分别提出，是一种支持量子纠错的纠错编码，在量子复杂性理论的应用中也具有重要价值。本文通过简短注记证明（线性、完美）零知识编码与量子CSS码具有等价性。我们通过利用该等价性构造显式的渐近优零知识局部可测试码，展示了这一等价关系的应用潜力。