Flag Invariants of Rank Metric Codes (joint work with Dr. John Sheekey, Dr. Eimear Byrne)
Vortrag von Arani Paul
Datum: 06.05.26 Zeit: 16.30 - 17.30 Raum: UNINE, B217
The problem of determining when two Fq^m -linear rank-metric codes are equivalent is important for reasons of both mathematical interest and for practical applications. Even though this problem can be efficiently solved computationally [2], finding structural properties that remain invariant under equivalence remains an active line of research. One of the main reasons behind that is the computational hardness of existing invariants, which act as distinguishers between equivalence classes. Beyond initial considerations such as minimum distance and weight enumerators, one of the most well-studied invariants is the generalised weights of a code [1, 3].
In this talk we introduce a new invariant for vector rank metric codes based on the support dimensions of complete flags of subcodes. We will demonstrate that these invariants are related to the generalised weights, but that they are both different and comparatively easier to compute than the generalised weights. We also relate the new invariants to the corresponding q-system of the code.
References:
[1] T. H. Randrianarisoa. A geometric approach to rank metric codes and a classification of constant weight codes. Designs, Codes and Cryptography, 88:1331–1348, 2020
[2] A. Couvreur, T. Debris-Alazard, and P. Gaborit. On the hardness of code equivalence problems in rank metric. arXiv:2011.04611, 2020.
[3] G. Marino, A. Neri, and R. Trombetti. Evasive subspaces, generalized rank weights and near mrd codes. Discrete Mathematics, 346(12):113605, 2023.