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

Hamada, Noboru; Maruta, Tatsuya; Oya, Yusuke

Serdica Journal of Computing (2012)

- Volume: 6, Issue: 3, page 253-266
- ISSN: 1312-6555

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topHamada, 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 -

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