{"id":{"repo_id":"brock","oai_identifier":"oai:brocku.scholaris.ca:10464/4106"},"canonical_url":"https://search.dev.ndltd.org/etd/brock/oai:brocku.scholaris.ca:10464/4106","repository":{"repo_id":"brock","name":"Brock University","base_url":"https://brocku.scholaris.ca/server/oai/request"},"display":{"title":"Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes","abstract":"Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.","abstract_html":"Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.","abstract_has_math":false,"creators":["Derka, Martin"],"institution":"Brock University","degree_name":"M.Sc. Computer Science","degree_level":"Masters","degree_discipline":"Faculty of Mathematics and Science","degree_department":"Department of Computer Science","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-09-18","date_published":"2012-09-18","updated_at":"2026-07-24T01:23:04Z","subjects":["Error-correcting codes","Type II codes","Automorphism group","Permutation"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10464/4106","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Department of Computer Science"]},{"key":"dc:creator","label":"Author","values":["Derka, Martin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-09-18T15:01:49Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2012-09-18T15:01:49Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-09-18"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Faculty of Mathematics and Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.Sc. 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Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map."]},{"key":"dc:title","label":"Title","values":["Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes"]}]}],"canonical_facts":{"dc:contributor.department":["Department of Computer Science"],"dc:creator":["Derka, Martin"],"dc:date.accessioned":["2012-09-18T15:01:49Z"],"dc:date.available":["2012-09-18T15:01:49Z"],"dc:date.issued":["2012-09-18"],"dc:description.abstract":["Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map."],"dc:identifier.uri":["http://hdl.handle.net/10464/4106"],"dc:language.iso":["eng"],"dc:subject":["Error-correcting codes","Type II codes","Automorphism group","Permutation"],"dc:title":["Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Faculty of Mathematics and Science"],"thesis:degree_level":["Masters"],"thesis:degree_name":["M.Sc. Computer Science"],"thesis:institution_name":["Brock University"]},"updated_at":"2026-07-24T01:23:04Z"}