Codes with extremality properties in the rank metric

Vortrag von Cristina Landolina

Datum: 16.02.22  Zeit: 15.00 - 16.00  Raum:

Codes in the rank metric were first discovered 1978 by Delsarte. These codes have attracted attention lately due to their considerabile list of applications. A rank-metric code can be considered as an F_q-linear space of n times m matrices over the finite field of q elements. Several bounds relating the parameters of a rank-metric code can be derived. We will discuss the Anticode bound relating the dimension of a code with its maximum rank. To this end we will present the classification of Optimal Anticodes, which are codes attaining this bound. A new, more general Anticode bound is presented. We will study and completely classify a larger family of rank-metric codes attaining this new bound. This codes are called (dually) quasi Optimal Anticodes. Moreover we will show how invariants such as the generalized weights and the rank distribution of (dually) quasi Optimal Anticodes can be easily derived from the structural classification of the latter.

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