A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications
Data(s) |
03/12/2012
03/12/2012
2012
|
---|---|
Resumo |
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 supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138. |
Identificador |
Serdica Journal of Computing, Vol. 6, No 3, (2012), 253p-266p 1312-6555 |
Idioma(s) |
en |
Publicador |
Institute of Mathematics and Informatics Bulgarian Academy of Sciences |
Palavras-Chave | #(n, r)-arcs #Projective Plane #Linear Codes |
Tipo |
Article |