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A Maximal arc in a finite projective plane is a largest possible (''k'',''d'')-arc in that projective plane. If the finite projective plane has order ''q'' (there are ''q''+1 points on any line), then for a maximal arc, ''k'', the number of points of the arc, is the maximum possible (= ''qd'' + ''d'' - ''q'') with the property that no ''d''+1 points of the arc lie on the same line. ==Definition== Let be a finite projective plane of order ''q'' (not necessarily desarguesian). Maximal arcs of ''degree'' ''d'' ( 2 ≤ ''d'' ≤ ''q''- 1) are (''k'',''d'')-arcs in , where ''k'' is maximal with respect to the parameter ''d'', in other words, ''k'' = ''qd'' + ''d'' - ''q''. Equivalently, one can define maximal arcs of degree ''d'' in as non-empty sets of points ''K'' such that every line intersects the set either in 0 or ''d'' points. Some authors permit the degree of a maximal arc to be 1, ''q'' or even ''q''+ 1. Letting ''K'' be a maximal (''k'', ''d'')-arc in a projective plane of order ''q'', if * ''d'' = 1, ''K'' is a point of the plane, * ''d'' = ''q'', ''K'' is the complement of a line (an affine plane of order ''q''), and * ''d'' = ''q'' + 1, ''K'' is the entire projective plane. All of these cases are considered to be ''trivial'' examples of maximal arcs, existing in any type of projective plane for any value of ''q''. When 2 ≤ ''d'' ≤ ''q''- 1, the maximal arc is called ''non-trivial'', and the definition given above and the properties listed below all refer to non-trivial maximal arcs. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maximal arc」の詳細全文を読む スポンサード リンク
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