TY - GEN
T1 - Efficient Decoding of Gabidulin Codes over Galois Rings
AU - Puchinger, Sven
AU - Renner, Julian
AU - Wachter-Zeh, Antonia
AU - Zumbrage, Jens
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity in the code length. The new method consists of two steps: (1) solving a syndrome-based key equation to obtain the annihilator polynomial of the error and therefore the column space of the error, (2) solving a key equation based on the received word in order to reconstruct the error vector. This two-step approach became necessary since standard solutions as the Euclidean algorithm do not properly work over rings.
AB - This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity in the code length. The new method consists of two steps: (1) solving a syndrome-based key equation to obtain the annihilator polynomial of the error and therefore the column space of the error, (2) solving a key equation based on the received word in order to reconstruct the error vector. This two-step approach became necessary since standard solutions as the Euclidean algorithm do not properly work over rings.
UR - http://www.scopus.com/inward/record.url?scp=85115116749&partnerID=8YFLogxK
U2 - 10.1109/ISIT45174.2021.9517904
DO - 10.1109/ISIT45174.2021.9517904
M3 - Conference contribution
AN - SCOPUS:85115116749
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 25
EP - 30
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 -