More on MRD codes

Talk by Prof. Dr. Wolfgang Willems

Speaker invited by: Prof. Dr. Joachim Rosenthal

Date: 01.03.17  Time: 16.00 - 17.00  Room: Y27H28

The first part of the talk deals with completely reducible MRD codes C in F_^{m×n}, i.e., C splits up into a direct sum of simple MRD codes. We prove that an MRD code is always completely reducible if it can be obtained from a classical code in F_^{m×n}. The second part is devoted to self-dual MRD codes. Here we prove that a Gabidulin code G ≤ F_^{m×n} is equivalent to a self-dual MRD code if and only if dim G = n^2/2, n ≡ 2 mod 4 and q ≡ 3 mod 4. During the talk we discuss many open problems concerning completely reducible and self-dual MRD codes.