Show simple item record Mavron, V. C. McDonough, Thomas Key, Jennifer D. 2010-12-07T09:07:24Z 2010-12-07T09:07:24Z 2009-01
dc.identifier.citation Mavron , V C , McDonough , T & 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 . DOI: 10.1016/j.ejc.2008.01.003 en
dc.identifier.issn 1095-9971
dc.identifier.other PURE: 154779
dc.identifier.other PURE UUID: 90049e65-721d-4a3e-b143-86d9652dc203
dc.identifier.other dspace: 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.rights en
dc.title An upper bound for the minimum weight of the dual codes of desarguesian planes en
dc.type /dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article en
dc.contributor.institution Algebraic Combinatorics en
dc.contributor.institution Department of Physics en
dc.description.status Peer reviewed en

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