论文标题
超越Guruswami-Sudan（和Parvaresh-vardy）半径：折叠的芦苇 - 固体，多样性和衍生物代码
Beyond the Guruswami-Sudan (and Parvaresh-Vardy) Radii: Folded Reed-Solomon, Multiplicity and Derivative Codes
论文作者
论文摘要
经典的芦苇 - 固体代码的家族包括对有限字段$ \ mathbb {f} _q $度的多项式评估，小于$ k $，在$ n $ dinters election elements。这些可以说是最广泛使用和研究的代码，因为它们具有擦除和错误校正功能，以及许多其他良好的属性。在这项调查中，我们研究了密切相关的代码，折叠的芦苇 - 固体代码，这是实现列表解码能力的第一个建设性代码。然后，我们研究了另外两个具有此功能的代码，\ textIt {MuluteDity cod}和\ textIt {derivative codes}。我们的重点大部分是对这些代码的解码算法的列表，尽管我们还研究了多样性代码的局部解论性。
The classical family of Reed-Solomon codes consist of evaluations of polynomials over the finite field $\mathbb{F}_q$ of degree less than $k$, at $n$ distinct field elements. These are arguably the most widely used and studied codes, as they have both erasure and error-correction capabilities, among many others nice properties. In this survey we study closely related codes, folded Reed-Solomon codes, which are the first constructive codes to achieve the list decoding capacity. We then study two more codes which also have this feature, \textit{multiplicity codes} and \textit{derivative codes}. Our focus for the most part are the list decoding algorithms of these codes, though we also look into the local decodability of multiplicity codes.
