Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric


Séminaire AMAC: CASC

10/03/2022 - 09:30 Elisa Lorenzo Garcia (Université de Neuchâtel) IMAG 106

Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric. In this talk, I will give an Anticode Bound for the sum-rank metric, which extends the corresponding Hamming and rank-metric Anticode bounds. Later I will classify optimal anticodes, i.e. codes attaining the sum-rank metric Anticode Bound. I will use these optimal anticodes to define generalized sum-rank weights and study their main properties. In particular, I will prove that the generalized weights of an MSRD code are determined by its parameters. As an application, I will explain how generalized weights measure information leakage in multishot network coding.

Joint work with E. Camps Moreno, E. Gorla, C. Landolina, U. Martínez-Peñas and F. Salizzoni