An Explicit Construction of Universally Decodable Matrices
| dc.creator | Vontobel, Pascal O. | |
| dc.creator | Ganesan, Ashwin | |
| dc.date | 2005-08-23 | |
| dc.date.accessioned | 2026-07-07T08:15:36Z | |
| dc.date.available | 2026-07-07T08:15:36Z | |
| dc.description | Universally decodable matrices can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $n$ and a prime power $q$. Based on Pascal's triangle we give an explicit construction of universally decodable matrices for any non-zero integers $L$ and $n$ and any prime power $q$ where $L \leq q+1$. This is the largest set of possible parameter values since for any list of universally decodable matrices the value $L$ is upper bounded by $q+1$, except for the trivial case $n = 1$. For the proof of our construction we use properties of Hasse derivatives, and it turns out that our construction has connections to Reed-Solomon codes, Reed-Muller codes, and so-called repeated-root cyclic codes. Additionally, we show how universally decodable matrices can be modified so that they remain universally decodable matrices. | |
| dc.identifier | https://arxiv.org/abs/cs/0508098 | |
| dc.identifier | http://arxiv.org/abs/cs/0508098 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133496 | |
| dc.subject | Information Theory | |
| dc.subject | Discrete Mathematics | |
| dc.title | An Explicit Construction of Universally Decodable Matrices | |
| dc.type | text |