{"id":{"repo_id":"texas","oai_identifier":"oai:repositories.lib.utexas.edu:2152/2962"},"canonical_url":"https://search.dev.ndltd.org/etd/texas/oai:repositories.lib.utexas.edu:2152/2962","repository":{"repo_id":"texas","name":"University of Texas","base_url":"https://repositories.lib.utexas.edu/server/oai/request"},"display":{"title":"Error-correcting codes on low néron-severi rank surfaces","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Zarzar, Marcos Augusto"],"institution":"The University of Texas at Austin","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Voloch, José Felipe"],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006","date_published":"2006","updated_at":"2026-07-24T05:00:56Z","subjects":[],"languages":["eng"],"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."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["b68655204"],"render_values":[{"text":"b68655204","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2152/2962","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Voloch, José Felipe"]},{"key":"dc:creator","label":"Author","values":["Zarzar, Marcos Augusto"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2008-08-28T23:18:54Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2008-08-28T23:18:54Z"]},{"key":"dc:date.issued","label":"Date","values":["2006"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The University of Texas at Austin"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["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."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["b68655204"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/2152/2962"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["electronic"]},{"key":"dc:title","label":"Title","values":["Error-correcting codes on low néron-severi rank surfaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Voloch, José Felipe"],"dc:creator":["Zarzar, Marcos Augusto"],"dc:date.accessioned":["2008-08-28T23:18:54Z"],"dc:date.available":["2008-08-28T23:18:54Z"],"dc:date.issued":["2006"],"dc:description.abstract":["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."],"dc:format.medium":["electronic"],"dc:identifier":["b68655204"],"dc:identifier.uri":["http://hdl.handle.net/2152/2962"],"dc:language.iso":["eng"],"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."],"dc:title":["Error-correcting codes on low néron-severi rank surfaces"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The University of Texas at Austin"]},"updated_at":"2026-07-24T05:00:56Z"}