A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

Hamada, Noboru, Maruta, Tatsuya, and Oya, Yusuke. "A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications." Serdica Journal of Computing 6.3 (2012): 253-266. <http://eudml.org/doc/219607>.

@article{Hamada2012,
abstract = {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.},
author = {Hamada, Noboru, Maruta, Tatsuya, Oya, Yusuke},
journal = {Serdica Journal of Computing},
keywords = {(n, r)-arcs; Projective Plane; Linear Codes; -arcs; projective plane; linear codes},
language = {eng},
number = {3},
pages = {253-266},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications},
url = {http://eudml.org/doc/219607},
volume = {6},
year = {2012},
}

TY - JOUR
AU - Hamada, Noboru
AU - Maruta, Tatsuya
AU - Oya, Yusuke
TI - A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications
JO - Serdica Journal of Computing
PY - 2012
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 6
IS - 3
SP - 253
EP - 266
AB - 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.
LA - eng
KW - (n, r)-arcs; Projective Plane; Linear Codes; -arcs; projective plane; linear codes
UR - http://eudml.org/doc/219607
ER -