We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.

ACM Computing Classification System (1998): E.4.
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.
This...

Download Results (CSV)