Vortrag
A general theory of supports and generalized weights for linear codes
Vortrag von Prof. Dr. Elisa Gorla
Datum: 08.03.23 Zeit: 16.30 - 17.30 Raum:
In this talk, I propose a general definition of supports for linear codes over finite fields, and more generally over finite commutative rings. A support induces a weight function, a distance, and generalized weights. I discuss the properties of the generalized weights, showing that some properties of the Hamming support have a natural generalization. In particular, it is well-known that the matroid associated to a linear block code via its parity check matrix determines the generalized weights of the code with respect to the Hamming support. In this more general setting, I associate to a code a monomial ideal, whose algebraic invariants determine the generalized weights of the code. In the case of a linear code with the Hamming support, this ideal is the Stanley-Reisner ideal of the matroid associated to the code. No prior knowledge of commutative algebra will be assumed during the talk. The talk is based on joint work with Alberto Ravagnani.
(**This eSeminar will take place over Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact zita.fiquelideabreu@math.uzh.ch **)