List-decoding and list-recovery are important generalizations of unique decoding and receive considerable attention over the years. We study the optimal trade-off among the list-decoding (resp. list-recovery) radius, the list size, and the code rate, when the list size is constant and the alphabet size is large (both compared with the code length). We prove a new Singleton-type bound for list-decoding, which, for a wide range of parameters, is asymptotically tight up to a $1+o(1)$ factor. We also prove a Singleton-type bound for list-recovery, which is the first such bound in the literature. We apply these results to obtain near optimal lower bounds on the list size for list-decodable and list-recoverable codes with rates approaching capacity.

Moreover, we show that under some indivisibility condition of the parameters and over a sufficiently large alphabet, the largest list-decodable nonlinear codes can have much more codewords than the largest list-decodable linear codes. Such a large gap is not known to exist in unique decoding. We prove this by a novel connection between list-decoding and the notion of sparse hypergraphs in extremal combinatorics.

Lastly, we show that list-decodability or recoverability implies in some sense good unique decodability.

列表解码和列表恢复是独特解码的重要概括，多年来受到了相当多的关注。我们研究当列表大小恒定且字母表大小较大（均与代码长度相比）时列表解码（或列表恢复）半径、列表大小和码率之间的最佳权衡。我们证明了一种新的用于列表解码的单例类型界限，对于广泛的参数，它是渐近紧密的$1+哦（1）$因素。我们还证明了列表恢复的单例类型界限，这是文献中第一个这样的界限。我们应用这些结果来获得列表可解码和列表可恢复代码的列表大小的接近最佳下限，并且速率接近容量。

此外，我们表明，在参数的某些不可分性条件下和在足够大的字母表上，最大列表可解码非线性码可以比最大列表可解码线性码具有更多的码字。如此大的差距在独特的解码中并不存在。我们通过列表解码和极值组合中的稀疏超图概念之间的新颖联系来证明这一点。

最后，我们表明列表可解码性或可恢复性在某种意义上意味着良好的独特可解码性。