Next talk: June, 18th - Prasant Singh
June, 18th: Prasant Singh, UiT the Arctic University of Norway
Title: Symmetric determinental codes
Abstract:
The talk is a continuation of Prof Trygve's talk in the Bergen seminar this April,
and of what he (at least) mentioned in the Algebra seminar last week, although the talk will be self-contained.
In this talk, we recall the definition of determinantal varieties in the space of symmetric matrices.
Restricting the definition to finite fields, we can consider the algebraic-geometric (AG) codes arising from these varieties.
We study some interesting properties of these codes and show that these codes have only a few distinct possible weights.
In the end, we discuss the minimum distance of these codes in the even rank case, i.e., in the case when the varieties
are the zero sets of minors of odd order of a generic symmetric matrix.
The talk is based on joint work with Prof. P. Beelen (DTU) and Prof. T. Johnsen.
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