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# A note on the stability number of an orthogonality graph.

 dc.contributor.author Klerk, Etienne de. dc.contributor.author Pasechnik, Dmitrii V. dc.date.accessioned 2011-07-06T03:35:01Z dc.date.available 2011-07-06T03:35:01Z dc.date.copyright 2006 dc.date.issued 2011-07-06T03:35:01Z dc.identifier.citation Klerk, E. D., & Pasechnik, D. V. (2006). A note on the stability number of an orthogonality graph. European Journal of Combinatorics, 28, 1971-1979. dc.identifier.uri http://hdl.handle.net/10220/6870 dc.description.abstract We consider the orthogonality graph Ω(n) with 2n vertices corresponding to the vectors {0, 1}n, two vertices adjacent if and only if the Hamming distance between them is n/2. We show that, for n = 16, the stability number of Ω(n) is α(Ω(16)) = 2304, thus proving a conjecture by Galliard [Classical pseudo telepathy and coloring graphs, Diploma Thesis, ETH Zurich, 2001. Available at http://math.galliard.ch/Cryptography/Papers/PseudoTelepathy/SimulationOfEntanglement.pdf]. The main tool we employ is a recent semidefinite programming relaxation for minimal distance binary codes due to Schrijver [New code upper bounds from the Terwilliger algebra, IEEE Trans. Inform. Theory 51 (8) (2005) 2859–2866]. As well, we give a general condition for Delsarte bound on the (co)cli¬ques in graphs of relations of association schemes to coincide with the ratio bound, and use it to show that for Ω(n) the latter two bounds are equal to 2n/n. dc.format.extent 10 p. dc.language.iso en dc.relation.ispartofseries European journal of combinatorics dc.rights © 2006 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by European Journal of Combinatorics, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at the following DOI: http://dx.doi.org/10.1016/j.ejc.2006.08.011. dc.subject DRNTU::Science::Mathematics::Geometry. dc.title A note on the stability number of an orthogonality graph. dc.type Journal Article dc.contributor.school School of Physical and Mathematical Sciences dc.identifier.doi http://dx.doi.org/10.1016/j.ejc.2006.08.011 dc.description.version Accepted version

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