A Characterization of Designs Related to the Witt System S(5, 8, 24).
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 research was partially...
Let denote the minimum cardinality of a ternary code of length and covering radius one. In a previous paper, we improved on the lower bound by showing that . In this note, we prove that .