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Non – existence of ( k, n; f ) – arcs of type (n – 3, n) in PG(2, 9) | ||
| basrah journal of science | ||
| Article 1, Volume 30, Issue 2, 2012, Pages 71-85 PDF (0 K) | ||
| Authors | ||
| Hussain and M. Y. Abass; F. K. Hameed; M. A. Abdul | ||
| Abstract | ||
| In this paper we proved that there is no ( 81, 12; f ) – arc of type ( 9, 12 ) in PG(2, 9) in which the points of weight 0 form ( 10, 3 ) – arc of type ( τ_3=9, τ_2=18, τ_1=37 and τ_0=27 ) or ( 10, 4 ) – arc of type ( τ_4=3, τ_3=0, τ_2=27, τ_1=34 and τ_0=27 ) with three non – concurrent 4 – secants . Also when the points of weight 0 form ( 10, 4 ) – arcs of types ( τ_4=2, τ_3=3, τ_2=24, τ_1=35 and τ_0=27 ) and ( τ_4=1, τ_3=6, τ_2=21, τ_1=36 and τ_0=27 ), there is no ( 81, 12; f ) – arc of type ( 9, 12 ) in PG(2, 9). We proved also there is no ( 76, 11; f ) – arcs of type (8, 11) in PG(2, 9) when the points of weight 0 form ( 15, m ) – arcs in PG(2, 9) such that m = 3, 4, 5 . | ||
| Keywords | ||
| Projective plane; arcs; weighted arcs | ||
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