Tittle: Asymptotically good codes and matroid structure theory
| Speaker: | Peter Nelson |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract: 'Relative distance' and 'rate' are linear code parameters between 0 and 1 that, ideally, are as large as possible. Linear codes are essentially representable matroids, and both rate and relative distance have natural matroidal interpretations. I will discuss a result that applies a deep theorem in matroid structure theory to show that, if a class $\mathcal{C}$ of linear codes corresponds to a proper minor-closed subclass of the binary matroids, then large codes in $\mathcal{C}$ cannot simultaneously have rate and relative distance bounded away from zero; this shows that such a class $\mathcal{C}$ is not 'asymptotically good', substantially generalising a previous result due to Kashyap. This is joint work with Stefan van Zwam.