On some polynomials related to weight enumerators of linear codes (Q2784509)

The author discusses the relation between the polynomial invariants of codes and matroids. In particular he examines the relation between the weight enumerator polynomial of a linear code and the rank polynomial of the corresponding matroid, which is equivalent to Greene's theorem involving the Tutte polynomial of the matroid. This leads to an example dealing with the reliability polynomial of linear matroids in which the upper bounds for reliability are derived. A further connection between the weight enumerator polynomial and the partition polynomial of the Potts model of a finite graph is presented. NEWLINENEWLINENEWLINEReviewer's remark: Whereas the basic definitions concerning linear codes are provided, readers without any background in matroid theory may wish to consult a book on this topic [for example, \textit{D. J. A. Welsh}, Matroid theory (Academic Press; London) (1976; Zbl 0343.05002)] as this information for matroids is rather sparse.