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arXiv · 2102.03079

Bounds on List Decoding of Linearized Reed-Solomon Codes

Sven Puchinger·Johan Rosenkilde
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Abstract

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.

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Sven Puchinger, Johan Rosenkilde. 2021-02-05. Bounds on List Decoding of Linearized Reed-Solomon Codes. https://arxiv.org/abs/2102.03079

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