A linear code can be thought of as a vector matroid represented bythe columns of code's generator matrix; a well-known result in thiscontext is Greene's theorem on a connection of the weight polynomial ofthe code and the Tutte polynomial of the matroid. We examine thisconnection from the coding-theoretic viewpoint, building upon the rankpolynomial of the code. This enables us to: (1) relate the weightpolynomial of codes and the reliability polynomial of linear matroidsand to prove new bounds on the latter; (2) prove that the partitionpolynomial of the Potts model equals the weight polynomial of thecocycle code of the underlying graph; (3) give a simple proof ofGreene's theorem and its generalization
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