Geodesic
Projective Geometries that are Disjoint Unions of Caps
Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1299-1305

Voir la notice de l'article provenant de la source Cambridge University Press

We show that any PG(2n, q2) is a disjoint union of (q 2n+1 − 1)/ (q − 1) caps, each cap consisting of (q 2n+1 + 1)/(q + 1) points. Furthermore, these caps constitute the “large points” of a PG(2n, q), with the incidence relation defined in a natural way.A square matrix H = (h ij ) over the finite field GF(q2), q a prime power, is said to be Hermitian if h ij q = h ij for all i, j [1, p. 1161]. In particular, h ii ∈ GF(q). If if is Hermitian, so is p(H), where p(x) is any polynomial with coefficients in GF(q).Given a Desarguesian Projective Geometry PG(2n, q2), n > 0, we denote its points by column vectors: All Hermitian matrices in this paper will be 2n + 1 by 2n + 1, n > 0. 
Kestenband, Barbu C. Projective Geometries that are Disjoint Unions of Caps. Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1299-1305. doi: 10.4153/CJM-1980-099-7
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