Two-Weight Codes, Partial Geometries and Steiner Systems |
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Authors: | Frank De Clerck Mario Delanote |
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Institution: | (1) Ghent University—, Department of Pure Mathematics and Computer Algebra, Belgium |
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Abstract: | Two-weight codes and projectivesets having two intersection sizes with hyperplanes are equivalentobjects and they define strongly regular graphs. We construct projective sets in PG(2m – 1,q) that have the sameintersection numbers with hyperplanes as the hyperbolic quadricQ+(2m – 1,q). We investigate these sets; we provethat if q = 2 the corresponding strongly regular graphsare switching equivalent and that they contain subconstituentsthat are point graphs of partial geometries. If m = 4the partial geometries have parameters s = 7, t = 8, = 4 and some of them are embeddable in Steinersystems S(2,8,120). |
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Keywords: | Seidel switching strongly regular graphs partial geometries Steiner systems two-weight codes |
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