A nice proof of Wei's duality theorem

Abstract: 

The Tutte polynomial was once an esoteric object known only to the then small community of combinatorialists. That changed when Greene (1976) pointed out the connection between this polynomial and weight enumerators, and how that connection provided a beautifully simple proof of the MacWilliams Identity (MacWilliams 1963) of coding theory fame. The Tutte polynomial is now of wide interest and appeal to the broader mathematical community who have found it lurking disguised in numerous areas of mathematics. Despite its present prominence, few are aware of how the Tutte polynomial provides another beautifully simple proof of a second celebrated duality theorem from coding theory, namely Wei’s Duality Theorem (Wei 1991). This proof, due to Duursma (2004), deserves better exposure, so this talk will present Duursma’s proof.