| EPSRC Reference: |
GR/L88764/01 |
| Title: |
TRELLIS STRUCTURE OF ALGEBRAIC-GEOMETRIC CODES |
| Principal Investigator: |
Norton, Dr G |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Electrical and Electronic Engineering |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 1998 |
Ends: |
31 March 2001 |
Value (£): |
118,088
|
| EPSRC Research Topic Classifications: |
| Digital Signal Processing |
|
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
We propose studying the structure and complexity of trellises of Algebraic Geometry (AG) codes. (Trellis Theory of (Generalised) Reed Muller (GRM), Berman and other codes have been investigated on a current grant. AG codes are now accessible in standard texts e.g. Stichtenoth). So far, these two topics have been studied separately. The approach will be to begin with the relatively simple Klein-Quartic and Hermitian codes, progressing to more complex Artin-Schreier Tower codes and AG codes from classical varieties, which includes GRM codes. We expect the Riemann-Roch Theorem to yield a general lower bound for AG state complexity. Results can be compared to the known Generalised Hamming Weight Hierarchy of many AG codes, which provides a lower bound for state complexity. The MSGM can be computed in MAPLE from any generator matrix. This will provide a useful test for results on the general form of the MSGM's of e.g. Hermitian codes, or perhaps a subfamily. Such an MSGM can be used to determine parallel subtrellises of minimal and non-minimal trellises for faster decoding of e.g. Hermitian codes. This research has the potential of giving efficient, practical soft-decision decoders of powerful new error-correcting codes, which outperform Reed-Solomon codes, for example.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.bris.ac.uk |