MacWilliams identity for codes with the rank metric
EURASIP Journal on Wireless Communications and Networking - Advances in Error Control Coding Techniques
Designing a rank metric based mceliece cryptosystem
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Full cryptanalysis of the chen identification protocol
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Linear codes using skew polynomials with automorphisms and derivations
Designs, Codes and Cryptography
| Hi-index | 754.84 |
The rank distance was introduced by E.M. Gabidulin (see Probl. Pered. Inform., vol.21, p.1-12, 1985). He determined an upper bound for the minimum rank distance of a code. Moreover, he constructed a class of codes which meet this bound: the so-called Gabidulin codes. We first characterize the linear and semilinear isometries for the rank distance. Then we determine the isometry group and the permutation group of Gabidulin codes of any length. We give a characterization of equivalent Gabidulin codes. Finally, we prove that the number of equivalence classes of Gabidulin codes is exactly the number of equivalence classes of vector spaces of dimension n contained in GF(pm) under some particular relations.