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dc.contributor.author Mavron, V. C.
dc.contributor.author McDonough, Thomas P.
dc.contributor.author Key, Jennifer D.
dc.date.accessioned 2010-12-07T09:07:24Z
dc.date.available 2010-12-07T09:07:24Z
dc.date.issued 2009-01
dc.identifier.citation Mavron , V C , McDonough , T P & Key , J D 2009 , ' An upper bound for the minimum weight of the dual codes of desarguesian planes ' European Journal of Combinatorics , vol 30 , no. 1 , pp. 220-229 . , 10.1016/j.ejc.2008.01.003 en
dc.identifier.other PURE: 154779
dc.identifier.other dspace: 2160/5987
dc.identifier.uri http://hdl.handle.net/2160/5987
dc.description J.D.Key, T.P.McDonough and V.C.Mavron, An upper bound for the minimum weight of the dual codes of desarguesian planes. European Journal of Combinatorics, Volume 30 Issue 1, January, 2009, pp. 220-229. en
dc.description.abstract We show that a construction described in [K.L. Clark, J.D. Key, M.J. de Resmini, Dual codes of translation planes, European J. Combinatorics 23 (2002) 529–538] of small-weight words in the dual codes of finite translation planes can be extended so that it applies to projective and affine desarguesian planes of any order p^m where p is a prime, and m≥1. This gives words of weight 2p^m+1-(p^m-1)/(p-1) in the dual of the p-ary code of the desarguesian plane of order p^m, and provides an improved upper bound for the minimum weight of the dual code. The same will apply to a class of translation planes that this construction leads to; these belong to the class of André planes. We also found by computer search a word of weight 36 in the dual binary code of the desarguesian plane of order 32, thus extending a result of Korchmáros and Mazzocca [Gábor Korchmáros, Francesco Mazzocca, On (q+t)-arcs of type (0,2,t) in a desarguesian plane of order q, Math. Proc. Cambridge Phil. Soc. 108 (1990) 445–459]. en
dc.format.extent 10 en
dc.language.iso eng
dc.relation.ispartof European Journal of Combinatorics en
dc.title An upper bound for the minimum weight of the dual codes of desarguesian planes en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.identifier.doi http://dx.doi.org/10.1016/j.ejc.2008.01.003
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.contributor.institution Algebraic Combinatorics en
dc.description.status Peer reviewed en


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