On multiple caps in finite projective spaces

In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the size of such caps. Furthermore, we generalize two product constructions for (k, 2)-caps to caps with larger n. We give explicit constructions for good caps with small n. In particular, we determine the largest size of a (k, 3)-cap in PG(3, 5), which turns out to be 44. The results on caps in PG(3, 5) provide a solution to four of the eight open instances of the main coding theory problem for q = 5 and k = 4. Mathematics Subject Classification: 51E22, 94B05, 94B65

• Type: Journal
• Year: 2010
• Where: DCC
• Authors: Yves Edel, Ivan N. Landjev
• Keywords: Computer Graphics, DCC 2010, Explicit Constructions, Lower Bound, Product Constructions