# Algebra Seminar

Title: Generalized minimum distance functions for schemes and linear codes

Abstract In coding theory, a linear code is a subspace of a finite dimensional vector space. To a linear code one can associate a set of points in projective space. If these points are distinct, then the Hamming distance of the code can be computed based on the geometry of the points.

Motivated by these considerations, we introduce commutative algebraic generalizations for the notion of Hamming distance, which are better suited for working with non-reduced schemes. We describe the properties of these generalized minimum distance functions, as well as bounding them in the spirit of the classical singleton bound and by means of a Cayley Bacharach-type conjecture.

This talk is based on joint work with Susan Cooper, Stefan Tohaneanu, Maria Vaz Pinto and Rafael Villarreal.