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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Barg, A. |
| Copyright Year | 2000 |
| Description | Author affiliation: Lucent Technol. Bell Labs., Murray Hill, NJ, USA (Barg, A.) |
| Abstract | A linear code can be thought of as a vector matroid represented by the columns of 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: (1) relate the weight polynomial of codes and the reliability polynomial of linear matroids and to prove new bounds on the latter; (2) prove that the partition polynomial of the Potts model equals the weight polynomial of the cocycle code of the underlying graph; (3) give a simple proof of Greene's theorem and its generalization. |
| File Size | 105045 |
| File Format | |
| ISBN | 0780358570 |
| DOI | 10.1109/ISIT.2000.866291 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2000-06-25 |
| Publisher Place | Italy |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Polynomials Linear code Vectors Combinatorial mathematics Upper bound Radio access networks Reliability theory Hamming weight Terminology Ear |
| Content Type | Text |
| Resource Type | Article |
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