Codes related to caps and the non-existence of some Griesmer codes
Assia Rousseva, Ivan Landjev · 2020
In this paper we consider the problem of class with parameters (q3+ 2q2+ q + 2, q2+ 2q + 2) in PG(3, q). Such arcs correspond to Griesmer [q3+ 2q2+ q + 2, 4, q3+ q2-q]q-codes. They are trivially obtained as the sum of a maximal cap in PG(3, q) and the whole geometry. We prove that for q = 5, 7 this is the only possible construction. This was known to be the case also for q = 4. For q = 3, there exists one further example. The characterization uses a divisibility result for plane blocking sets with parameters (q2, q-1) which is of independent interest.