An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters [n,k,d] and the list size L. L-MDS codes are then defined as codes that attain this bound (under a slightly stronger notion of list decodability), with 1-MDS codes corresponding to ordinary linear MDS codes. Several properties of such codes are presented; in particular, it is shown that the 2-MDS property is preserved under duality. Finally, explicit constructions for 2-MDS codes are presented through generalized Reed-Solomon (GRS) codes.

翻译：在线性代码的解码半径清单中,用编码参数[n,k,d]和清单大小L.-MDS编码被定义为达到这一约束的编码(根据略微增强的清单可变性概念),1-MDS编码相当于普通的线性MDS编码。这些编码的一些属性被显示为2-MDS属性的双重性。最后,2-MDS编码的明确构造通过通用Reed-Solomon(GRS)编码显示。