TY - GEN
T1 - Invariants and Inequivalence of Linear Rank-Metric Codes
AU - Neri, Alessandro
AU - Puchinger, Sven
AU - Horlemann-Trautmann, Anna Lena
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. These invariants give rise to an easily computable criterion to check if two codes are inequivalent. With this criterion we then derive bounds on the number of equivalence classes of classical and twisted Gabidulin codes.
AB - We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. These invariants give rise to an easily computable criterion to check if two codes are inequivalent. With this criterion we then derive bounds on the number of equivalence classes of classical and twisted Gabidulin codes.
KW - Code Equivalence
KW - Gabidulin Codes
KW - Rank-Metric Codes
KW - Twisted Gabidulin Codes
UR - http://www.scopus.com/inward/record.url?scp=85073150930&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2019.8849525
DO - 10.1109/ISIT.2019.8849525
M3 - Conference contribution
AN - SCOPUS:85073150930
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2049
EP - 2053
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -