Show simple item record V. C. en_US Thomas P. en_US Jennifer D. en_US 2010-12-07T09:07:24Z 2010-12-07T09:07:24Z 2009-01 en_US
dc.identifier en_US
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_US
dc.identifier.other PURE: 154779 en_US
dc.identifier.other dspace: 2160/5987 en_US
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_US
dc.format.extent 10 en_US
dc.relation.ispartof European Journal of Combinatorics en_US
dc.title An upper bound for the minimum weight of the dual codes of desarguesian planes en_US
dc.contributor.pbl Institute of Mathematics & Physics (ADT) en_US
dc.contributor.pbl Algebraic Combinatorics en_US

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