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dc.contributor.authorDerka, Martin
dc.date.accessioned2012-09-18T15:01:49Z
dc.date.available2012-09-18T15:01:49Z
dc.date.issued2012-09-18
dc.identifier.urihttp://hdl.handle.net/10464/4106
dc.description.abstractSelf-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 In addition, we present so far unpublished construction of the extended Golay code by P. Becker.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.en_US
dc.language.isoengen_US
dc.publisherBrock Universityen_US
dc.subjectError-correcting codesen_US
dc.subjectType II codesen_US
dc.subjectAutomorphism groupen_US
dc.subjectPermutationen_US
dc.titleGenerator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codesen_US
dc.typeElectronic Thesis or Dissertationen_US
dc.degree.nameM.Sc. Computer Scienceen_US
dc.degree.levelMastersen_US
dc.contributor.departmentDepartment of Computer Scienceen_US
dc.degree.disciplineFaculty of Mathematics and Scienceen_US


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