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Probl. Peredachi Inf., 2011, Volume 47, Issue 3, Pages 3–9 (Mi ppi2050)  

This article is cited in 1 scientific paper (total in 1 paper)

Coding Theory

New $(n,r)$-arcs in $\mathrm{PG}(2,17)$, $\mathrm{PG}(2,19)$, and $\mathrm{PG}(2,23)$

R. Daskalov, E. Metodieva

Department of Mathematics, Technical University of Gabrovo, Bulgaria

Abstract: An $(n,r)$-arc is a set of $n$ points of a projective plane such that some $r$ but no $r+1$ of them are collinear. The maximum size of an $(n,r)$-arc in $\mathrm{PG}(2,q)$ is denoted by $m_r(2,q)$. In this paper a new $(95,7)$-arc, $(183,12)$-arc, and $(205,13)$-arc in $\mathrm{PG}(2,17)$ are constructed, as well as a $(243,14)$-arc and $(264,15)$-arc in $\mathrm{PG}(2,19)$. Likewise, good large $(n,r)$-arcs in $\mathrm{PG}(2,23)$ are constructed and a table with bounds on $m_r(2,23)$ is presented. In this way many new 3-dimensional Griesmer codes are obtained. The results are obtained by nonexhaustive local computer search.

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English version:
Problems of Information Transmission, 2011, 47:3, 217–223

Bibliographic databases:

UDC: 621.391.1+519.7
Received: 20.05.2010

Citation: R. Daskalov, E. Metodieva, “New $(n,r)$-arcs in $\mathrm{PG}(2,17)$, $\mathrm{PG}(2,19)$, and $\mathrm{PG}(2,23)$”, Probl. Peredachi Inf., 47:3 (2011), 3–9; Problems Inform. Transmission, 47:3 (2011), 217–223

Citation in format AMSBIB
\Bibitem{DasMet11}
\by R.~Daskalov, E.~Metodieva
\paper New $(n,r)$-arcs in $\mathrm{PG}(2,17)$, $\mathrm{PG}(2,19)$, and~$\mathrm{PG}(2,23)$
\jour Probl. Peredachi Inf.
\yr 2011
\vol 47
\issue 3
\pages 3--9
\mathnet{http://mi.mathnet.ru/ppi2050}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2896172}
\transl
\jour Problems Inform. Transmission
\yr 2011
\vol 47
\issue 3
\pages 217--223
\crossref{https://doi.org/10.1134/S003294601103001X}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855968195}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. W. P. Hirschfeld, E. V. D. Pichanick, “Bounds For Arcs of Arbitrary Degree in Finite Desarguesian Planes”, J. Comb Des., 24:4 (2016), 184–196  crossref  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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