Since the early 70's, there has been notable interest in studying how the matroids and Tutte polynomials of linear codes over finite fields determine properties of those codes. Greene's Theorem was an early highlight of this study, showing that the Tutte polynomial determines the weight enumerator of the code. Most of the big questions in this study have recently been answered, and a new chapter of research has begun, investigating related but deeper lines of research. This talk will describe our progress along these new lines of research. This talk requires only basic linear algebra knowledge.
Joint work with Trygve Johnsen, Keisuke Shiromoto and Thomas Westerbäck.