Toric codes over finite fields
| dc.creator | Joyner, David | |
| dc.date | 2002-08-21 | |
| dc.date | 2003-07-30 | |
| dc.date.accessioned | 2026-07-07T08:18:10Z | |
| dc.date.available | 2026-07-07T08:18:10Z | |
| dc.description | In this note, a class of error-correcting codes is associated to a toric variety associated to a fan defined over a finite field $\fff_q$, analogous to the class of Goppa codes associated to a curve. For such a ``toric code'' satisfying certain additional conditions, we present an efficient decoding algorithm for the dual of a Goppa code. Many examples are given. For small $q$, many of these codes have parameters beating the Gilbert-Varshamov bound. In fact, using toric codes, we construct a $(n,k,d)=(49,11,28)$ code over $\fff_8$, which is better than any other known code listed in Brouwer's on-line tables for that $n$ and $k$. | |
| dc.description | 20 pages, 1 figure Significant revisions to the last 2 sections | |
| dc.identifier | https://arxiv.org/abs/math/0208155 | |
| dc.identifier | http://arxiv.org/abs/math/0208155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134342 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Information Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 14M25;94B27 | |
| dc.title | Toric codes over finite fields | |
| dc.type | text |