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- W1984577366 abstract "A linear code can be thought of as a vector matroid represented by the columns of the code's generator matrix; a well-known result in this context is Greene's theorem on a connection of the weight polynomial of the code and the Tutte polynomial of the matroid. We examine this connection from the coding-theoretic viewpoint, building upon the rank polynomial of the code. This enables us to obtain bounds on all-terminal reliability of linear matroids and new proofs of two known results: Greene's theorem and a connection between the weight polynomial and the partition polynomial of the Potts model." @default.
- W1984577366 created "2016-06-24" @default.
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- W1984577366 date "2002-01-01" @default.
- W1984577366 modified "2023-10-18" @default.
- W1984577366 title "On Some Polynomials Related to Weight Enumerators of Linear Codes" @default.
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- W1984577366 doi "https://doi.org/10.1137/s0895480199364148" @default.
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