Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank metric). List decoding in these extreme cases is well-studied, and the two code classes behave very differently in terms of list size, but nothing is known for the general case. In this paper, we derive a lower bound on the list size for LRS codes, which is, for a large class of LRS codes, exponential directly above the Johnson radius. Furthermore, we show that some families of linearized Reed-Solomon codes with constant numbers of blocks cannot be list decoded beyond the unique decoding radius.
翻译：线性 Reed- Solomon (LRS) 代码是一成不变的公制代码, 以平等方式满足Soneton 约束。 在两个超强公制的极端情况下, 它们与Reed- Solomon 代码( Hamming 公制) 和 Gabidulin 代码( rent 公制 公制 ) 相吻合。 在这些极端情况下, 列表解码研究周全, 两个代码类别在列表大小上的表现非常不同, 但一般情况下却一无所知。 在本文中, 我们的LRS 代码在列表大小上得出了一个较低的约束, 对于一大批的 LRS 代码来说, 其指数直接高于 Johnson 半径。 此外, 我们显示, 一些具有恒定数字的线性 Reed- Solomon 代码的家族无法在独有解码半径之外进行解码 。
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