标题： 一种针对退化稳定子码的汉明类似界 显示英文标题

标题： A Hamming-Like Bound for Degenerate Stabilizer Codes

摘要： 量子汉明界最初被提出作为非退化量子码参数的上界，但过去几十年中，许多工作表明许多退化量子码也必须遵守这一界限。 在本文中，我们表明存在一个比量子汉明界更严格的类似汉明的界限，该界限适用于长度大于某个正整数$N(t)$的退化$t$-误差纠正的稳定子码。 我们证明该界限适用于所有单误差纠正的退化稳定子码，迫使几乎所有最优距离-3的稳定子码都是非退化的。 显示英文摘要

摘要： 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.