The quantum Hamming bound was originally put forward as an upper bound on the parameters of nondegenerate quantum codes, but over the past few decades much work has been done to show that many degenerate quantum codes must also obey this bound. In this paper, we show that there is a Hamming-like bound stricter than the quantum Hamming bound that applies to degenerate $t$-error-correcting stabilizer codes of length greater than some positive integer $N(t)$. We show that this bound holds for all single-error-correcting degenerate stabilizer codes, forcing all but a handful of optimal distance-3 stabilizer codes to be nondegenerate.

翻译：量子汉明界最初作为非简并量子码参数的上界提出，但过去数十年的研究表明，许多简并量子码也必须遵循这一界限。本文证明，存在一个比量子汉明界更严格的类汉明界，适用于长度大于某正整数 $N(t)$ 的简并 $t$ 纠错稳定子码。我们证明该界限对所有单纠错简并稳定子码成立，从而迫使除少数最优距离-3稳定子码外，其余均为非简并码。