Designs and their codes
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Hyperovals and unitals in Figueroa planes
European Journal of Combinatorics
Dual codes of translation planes
European Journal of Combinatorics
On Sets without Tangents in Galois Planes of Even Order
Designs, Codes and Cryptography
On (q + t, t)-Arcs of Type (0, 2, t)
Designs, Codes and Cryptography
A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49
Designs, Codes and Cryptography
Blocking Sets in Desarguesian Affine and Projective Planes
Finite Fields and Their Applications
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We show that a construction described in [K.L. Clark, J.D. Key, M.J. de Resmini, Dual codes of translation planes, European J. Combin. 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-1p-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 Andre 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 Korchmaros and Mazzocca [Gabor Korchmaros, Francesco Mazzocca, On (q+t)-arcs of type (0,2,t) in a desarguesian plane of order q, Math. Proc. Cambridge Philos. Soc. 108 (1990) 445-459].