TY - GEN
T1 - Recursive Decoding of Binary Rank Reed-Muller Codes and Plotkin Construction for Matrix Codes
AU - Couvreur, Alain
AU - Pratihar, Rakhi
N1 - Publisher Copyright:
© 2025 IEEE.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - We give a recursive decoding algorithm of the rank metric Reed-Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021 for the binary case, i.e., G= (Z/2 Z)m. In a broad range of parameters, this recursive decoding algorithm has better complexity compared to a recently proposed decoding algorithm based on Dickson matrices. Furthermore, imitating the recursive structure, we introduce a Plotkin-like construction of matrix rank metric codes over finite fields answering a long-standing open question. We also provide a decoding algorithm associated to this construction.
AB - We give a recursive decoding algorithm of the rank metric Reed-Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021 for the binary case, i.e., G= (Z/2 Z)m. In a broad range of parameters, this recursive decoding algorithm has better complexity compared to a recently proposed decoding algorithm based on Dickson matrices. Furthermore, imitating the recursive structure, we introduce a Plotkin-like construction of matrix rank metric codes over finite fields answering a long-standing open question. We also provide a decoding algorithm associated to this construction.
KW - Binary rank metric Reed-Muller codes
KW - Plotkin construction
KW - decoding
KW - matrix codes
UR - https://www.scopus.com/pages/publications/105021944690
U2 - 10.1109/ISIT63088.2025.11195602
DO - 10.1109/ISIT63088.2025.11195602
M3 - Conference contribution
AN - SCOPUS:105021944690
T3 - IEEE International Symposium on Information Theory - Proceedings
BT - ISIT 2025 - 2025 IEEE International Symposium on Information Theory, Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2025 IEEE International Symposium on Information Theory, ISIT 2025
Y2 - 22 June 2025 through 27 June 2025
ER -