The MDS Conjecture
Tuesday, May 12, 2015 - 2:00pm - 3:00pm
The motivating question behind the MDS conjecture is: what is the maximum size g(k,q) of a family of vectors in (F_q)^k (the k-dimensional vector space over the finite field F_q) so that any k vectors in the family form a basis of (F_q)^k? This question interests the coding theory, algebraic geometry, and finite geometry communities, and its importance is highlighted by a 00 prize offered for its solution by the Information Theory and Applications (ITA) center at UCSD (http://media.itsoc.org/isit2006/vardy/handout.pdf). We give an exposition using the language of matrices of Simeon Ball's recent solution to this question when q is prime. If time permits, we will discuss joint work in progress on this question with Simeon Ball and Jan De-Buele.