Error-correcting codes on low néron-severi rank surfaces

In this work we construct and estimate the parameters of error-correcting codes on algebraic surfaces whose N´eron-Severi group has low rank. If the rank of the N´eron-Severi group of a surface is 1, the intersection of this surface with an irreducible surface of lower degree will be an irreducible curve, and this allows the construction of ”good” codes and we can have a good estimate for its parameters. Surfaces with rank 1 and many points are not easy to find, but we are able to find some surfaces with low rank that gave us ”good” codes too. We also present an efficient decoding algorithm for such codes. It is based on the realization of the code as an LDPC code, and it was inpired by the Luby-Mitzenmacher algorithm.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The University of Texas at Austin

Year dc:date.issued

2006

Author dc:creator

• Zarzar, Marcos Augusto

Advisor dc:contributor.advisor

• Voloch, José Felipe

Statement dc:rights

• Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.

Language dc:language.iso

eng

Identifier

b68655204

OAI identifier oai:identifier

oai:repositories.lib.utexas.edu:2152/2962