Bounds on List Decoding of Linearized Reed-Solomon Codes
Information Theory
2021-02-08 v1 math.IT
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.
Cite
@article{arxiv.2102.03079,
title = {Bounds on List Decoding of Linearized Reed-Solomon Codes},
author = {Sven Puchinger and Johan Rosenkilde},
journal= {arXiv preprint arXiv:2102.03079},
year = {2021}
}