M. D. S. codes and arcs in projective spaces: a survey

Let C be a code of length k over an alphabet A of size q greather or equal 2. Having chosen m with 2 m  k we impose the following condition on C: no two words agree in as many as m positions. It then follows that |C| qm. If |C|=qm, then C is called a Maximum Distance Separable code (M.D.S. ... Ausführliche Beschreibung

1. Person: Joseph A. Thas verfasserin
Quelle: In Le Matematiche (01.11.1992)
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Veröffentlicht: 1992
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  Creative Commons License Source: Directory of Open Access Journals (DOAJ).
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520 |a Let C be a code of length k over an alphabet A of size q greather or equal 2. Having chosen m with 2 m  k we impose the following condition on C: no two words agree in as many as m positions. It then follows that |C| qm. If |C|=qm, then C is called a Maximum Distance Separable code (M.D.S. code). A k-arc in PG(n,q) is a set K of k points with k at least n+1 such that no n+1 points lie in a hyperplane. It can be shown that arcs and linear M.D.S. codes are equivalent objects. Here we give a survey of important results on k-arcs, in particular we survey the answers to three fundamental problems on arcs posed by B. Segre in 1955. 
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