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Paper Detail

Paper IDD1-S3-T2.1
Paper Title Bounds on List Decoding of Linearized Reed-Solomon Codes
Authors Sven Puchinger, Technical University of Munich, Germany; Johan Rosenkilde, GitHub Denmark Aps, Denmark
Session D1-S3-T2: Rank-Metric Codes II
Chaired Session: Monday, 12 July, 22:40 - 23:00
Engagement Session: Monday, 12 July, 23:00 - 23:20
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.