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dc.contributor.authorBeane, Maria Elizabethen
dc.date.accessioned2014-03-14T20:36:33Zen
dc.date.available2014-03-14T20:36:33Zen
dc.date.issued2011-04-28en
dc.identifier.otheretd-05122011-153554en
dc.identifier.urihttp://hdl.handle.net/10919/32676en
dc.description.abstractS(5,8,24) is one of the largest known Steiner systems and connects combinatorial designs, error-correcting codes, finite simple groups, and sphere packings in a truly remarkable way. This thesis discusses the underlying structure of S(5,8,24), its construction via the (24,12) Golay code, as well its automorphism group, which is the Mathieu group M24, a member of the sporadic simple groups. Particular attention is paid to the calculation of the size of automorphism groups of Steiner systems using the Orbit-Stabilizer Theorem. We conclude with a section on the sphere packing problem and elaborate on how the 8-sets of S(5,8,24) can be used to form Leech's Lattice, which Leech used to create the densest known sphere packing in 24-dimensions. The appendix contains code written for Matlab which has the ability to construct the octads of S(5,8,24), permute the elements to obtain isomorphic S(5,8,24) systems, and search for certain subsets of elements within the octads.en
dc.publisherVirginia Techen
dc.relation.haspartBeane_ME_T_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectSteiner Systemsen
dc.subjectError-Correcting Codesen
dc.subjectMathieu Groupsen
dc.subjectSphere Packingsen
dc.titleAn Introduction to S(5,8,24)en
dc.typeThesisen
dc.contributor.departmentMathematicsen
dc.description.degreeMaster of Scienceen
thesis.degree.nameMaster of Scienceen
thesis.degree.levelmastersen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineMathematicsen
dc.contributor.committeechairBrown, Ezra A.en
dc.contributor.committeememberRossi, John F.en
dc.contributor.committeememberShimozono, Mark M.en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05122011-153554/en
dc.date.sdate2011-05-12en
dc.date.rdate2011-06-01en
dc.date.adate2011-06-01en


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