American Institute of Mathematical Sciences

Advanced
February  2009, 3(1): 29-34. doi: 10.3934/amc.2009.3.29

On the uniqueness of (48,6)-arcs in PG(2,9)

Ayako Kikui 1, , Tatsuya Maruta 1, and  Yuri Yoshida 1,

1. 

Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan, Japan, Japan

Received  September 2008 Revised  November 2008 Published  January 2009

It is known that $m_6(2,9)=48$, where $m_r(2,q)$ denotes the maximum value of $m$ for which an $(m,r)$-arc exists in PG$(2,q)$. We prove that $(48,6)$-arcs in PG$(2,9)$ are unique up to projective equivalence.
Keywords: Arcs, projective spaces, linear codes, Griesmer bound..
Mathematics Subject Classification: Primary: 05B25, 51E21; Secondary: 94B05, 94B2.
Citation: Ayako Kikui, Tatsuya Maruta, Yuri Yoshida. On the uniqueness of (48,6)-arcs in PG(2,9). Advances in Mathematics of Communications, 2009, 3 (1) : 29-34. doi: 10.3934/amc.2009.3.29
[1]

J. De Beule, K. Metsch, L. Storme. Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound. Advances in Mathematics of Communications, 2008, 2 (3) : 261-272. doi: 10.3934/amc.2008.2.261
[2]

Thomas Honold, Ivan Landjev. The dual construction for arcs in projective Hjelmslev spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 11-21. doi: 10.3934/amc.2011.5.11
[3]

Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. Linear nonbinary covering codes and saturating sets in projective spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 119-147. doi: 10.3934/amc.2011.5.119
[4]

J. C. Alvarez Paiva and E. Fernandes. Crofton formulas in projective Finsler spaces. Electronic Research Announcements, 1998, 4: 91-100.

[5]

Michael Kiermaier, Matthias Koch, Sascha Kurz. $2$-arcs of maximal size in the affine and the projective Hjelmslev plane over $\mathbb Z$25. Advances in Mathematics of Communications, 2011, 5 (2) : 287-301. doi: 10.3934/amc.2011.5.287
[6]

Jesús Carrillo-Pacheco, Felipe Zaldivar. On codes over FFN$(1,q)$-projective varieties. Advances in Mathematics of Communications, 2016, 10 (2) : 209-220. doi: 10.3934/amc.2016001
[7]

Christine Bachoc, Alberto Passuello, Frank Vallentin. Bounds for projective codes from semidefinite programming. Advances in Mathematics of Communications, 2013, 7 (2) : 127-145. doi: 10.3934/amc.2013.7.127
[8]

Linda Beukemann, Klaus Metsch, Leo Storme. On weighted minihypers in finite projective spaces of square order. Advances in Mathematics of Communications, 2015, 9 (3) : 291-309. doi: 10.3934/amc.2015.9.291
[9]

Domenico Mucci. Maps into projective spaces: Liquid crystal and conformal energies. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 597-635. doi: 10.3934/dcdsb.2012.17.597
[10]

Roland D. Barrolleta, Emilio Suárez-Canedo, Leo Storme, Peter Vandendriessche. On primitive constant dimension codes and a geometrical sunflower bound. Advances in Mathematics of Communications, 2017, 11 (4) : 757-765. doi: 10.3934/amc.2017055
[11]

Srimanta Bhattacharya, Sushmita Ruj, Bimal Roy. Combinatorial batch codes: A lower bound and optimal constructions. Advances in Mathematics of Communications, 2012, 6 (2) : 165-174. doi: 10.3934/amc.2012.6.165
[12]

Jop Briët, Assaf Naor, Oded Regev. Locally decodable codes and the failure of cotype for projective tensor products. Electronic Research Announcements, 2012, 19: 120-130. doi: 10.3934/era.2012.19.120
[13]

Daniele Bartoli, Lins Denaux. Minimal codewords arising from the incidence of points and hyperplanes in projective spaces. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021061
[14]

Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Advances in Mathematics of Communications, 2010, 4 (1) : 69-81. doi: 10.3934/amc.2010.4.69
[15]

Florent Foucaud, Tero Laihonen, Aline Parreau. An improved lower bound for $(1,\leq 2)$-identifying codes in the king grid. Advances in Mathematics of Communications, 2014, 8 (1) : 35-52. doi: 10.3934/amc.2014.8.35
[16]

Carlos Munuera, Fernando Torres. A note on the order bound on the minimum distance of AG codes and acute semigroups. Advances in Mathematics of Communications, 2008, 2 (2) : 175-181. doi: 10.3934/amc.2008.2.175
[17]

Yael Ben-Haim, Simon Litsyn. A new upper bound on the rate of non-binary codes. Advances in Mathematics of Communications, 2007, 1 (1) : 83-92. doi: 10.3934/amc.2007.1.83
[18]

José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón. Cyclic and BCH codes whose minimum distance equals their maximum BCH bound. Advances in Mathematics of Communications, 2016, 10 (2) : 459-474. doi: 10.3934/amc.2016018
[19]

Daniele Bartoli, Adnen Sboui, Leo Storme. Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes. Advances in Mathematics of Communications, 2016, 10 (2) : 355-365. doi: 10.3934/amc.2016010
[20]

Paolo Gidoni, Alessandro Margheri. Lower bound on the number of periodic solutions for asymptotically linear planar Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 585-606. doi: 10.3934/dcds.2019024

2020 Impact Factor: 0.935

Tools

Metrics

  • PDF downloads (117)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy