A NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE OF AN (n, r)-ARC IN PG(2, q) AND ITS APPLICATIONS
نویسندگان
چکیده
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.
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تاریخ انتشار 2013