Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 6, No 3, (2012), 253p-266p
Let q be a prime or a prime power ≥ 3. The purpose of this
paper is to give a necessary and sufficient condition for the existence of
an (n, r)-arc in PG(2, q ) for given integers n, r and q using the geometric
structure of points and lines in PG(2, q ) for n > r ≥ 3. Using the geometric
method and a computer, it is shown that there exists no (34, 3) arc in
PG(2, 17), equivalently, there exists no [34, 3, 31] 17 code.