eSeminar: Bounds on List Decoding of Linearized Reed-Solomon Codes

Coding Theory and Cryptography Seminars

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 talk, 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. The results are joint work with Johan Rosenkilde.