Our main result is that a (k, p)-arc in PG(2, q), q = ph, with k ≥ qp - q + p - 1/2 4√q can be extended to a maximal arc. Combining this result with the recent Ball, Blokhuis, Mazzocca theorem about the non-existence of maximal arcs for p > 2, it gives an upper bound for the size of a (k, p)-arc. The method can be regarded as a generalization of B. Segre's method for proving similar embeddability theorems for k-arcs (that is when n = 2). It is based on associating an algebraic envelope containing the short lines to the (k, p)-arc. However, the construction of the envelope is independent of Segre's method using the generalization of Menelaus' theorem.
|Number of pages||12|
|Journal||Designs, Codes, and Cryptography|
|Publication status||Published - Dec 1 1999|
- (k, n)-arc
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics