TY - GEN
T1 - Bounds on List Decoding of Linearized Reed-Solomon Codes
AU - Puchinger, Sven
AU - Rosenkilde, Johan
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - 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.
AB - 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.
KW - Linearized Reed-Solomon Codes
KW - List Decoding
KW - Sum-Rank Metric
UR - http://www.scopus.com/inward/record.url?scp=85115061363&partnerID=8YFLogxK
U2 - 10.1109/ISIT45174.2021.9517777
DO - 10.1109/ISIT45174.2021.9517777
M3 - Conference contribution
AN - SCOPUS:85115061363
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 154
EP - 159
BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021
Y2 - 12 July 2021 through 20 July 2021
ER -