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Singer 8-arcs of Mathon type in PG(2,2⁷)

Frank De Clerck UGent, Stefaan De Winter UGent and Thomas Maes UGent (2012) DESIGNS CODES AND CRYPTOGRAPHY. 64(1-2). p.17-31
abstract
De Clerck et al. (J Comb Theory, 2011) counted the number of non-isomorphic Mathon maximal arcs of degree-8 in PG(2, 2 (h) ), h not equal 7 and prime. In this article we will show that in PG(2, 2(7)) a special class of Mathon maximal arcs of degree-8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a detailed description of these arcs, and then count the total number of non-isomorphic Mathon maximal arcs of degree-8. Finally we show that the special arcs found in PG(2, 2(7)) extend to two infinite families of Mathon arcs of degree-8 in PG(2, 2 (k) ), k odd and divisible by 7, while maintaining the nice property of admitting a Singer group.
Please use this url to cite or link to this publication:
author
organization
alternative title
Singer 8-arcs of Mathon type in PG(2,2^7)
Singer 8-arcs of Mathon type in PG(2,2(7))
year
type
journalArticle (original)
publication status
published
subject
keyword
MAXIMAL ARCS, ODD, Maximal arcs, Hyperovals, DESARGUESIAN PLANES
journal title
DESIGNS CODES AND CRYPTOGRAPHY
Designs Codes Cryptogr.
volume
64
issue
1-2
pages
17 - 31
Web of Science type
Article
Web of Science id
000303512700003
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.779 (2012)
JCR rank
113/247 (2012)
JCR quartile
2 (2012)
ISSN
0925-1022
DOI
10.1007/s10623-011-9502-4
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2130112
handle
http://hdl.handle.net/1854/LU-2130112
date created
2012-06-04 09:23:46
date last changed
2012-06-18 15:38:02
@article{2130112,
  abstract     = {De Clerck et al. (J Comb Theory, 2011) counted the number of non-isomorphic Mathon maximal arcs of degree-8 in PG(2, 2 (h) ), h not equal 7 and prime. In this article we will show that in PG(2, 2(7)) a special class of Mathon maximal arcs of degree-8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a detailed description of these arcs, and then count the total number of non-isomorphic Mathon maximal arcs of degree-8. Finally we show that the special arcs found in PG(2, 2(7)) extend to two infinite families of Mathon arcs of degree-8 in PG(2, 2 (k) ), k odd and divisible by 7, while maintaining the nice property of admitting a Singer group.},
  author       = {De Clerck, Frank and De Winter, Stefaan and Maes, Thomas},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keyword      = {MAXIMAL ARCS,ODD,Maximal arcs,Hyperovals,DESARGUESIAN PLANES},
  language     = {eng},
  number       = {1-2},
  pages        = {17--31},
  title        = {Singer 8-arcs of Mathon type in PG(2,2\unmatched{2077})},
  url          = {http://dx.doi.org/10.1007/s10623-011-9502-4},
  volume       = {64},
  year         = {2012},
}

Chicago
De Clerck, Frank, Stefaan De Winter, and Thomas Maes. 2012. “Singer 8-arcs of Mathon Type in PG(2,27).” Designs Codes and Cryptography 64 (1-2): 17–31.
APA
De Clerck, Frank, De Winter, S., & Maes, T. (2012). Singer 8-arcs of Mathon type in PG(2,27). DESIGNS CODES AND CRYPTOGRAPHY, 64(1-2), 17–31.
Vancouver
1.
De Clerck F, De Winter S, Maes T. Singer 8-arcs of Mathon type in PG(2,27). DESIGNS CODES AND CRYPTOGRAPHY. 2012;64(1-2):17–31.
MLA
De Clerck, Frank, Stefaan De Winter, and Thomas Maes. “Singer 8-arcs of Mathon Type in PG(2,27).” DESIGNS CODES AND CRYPTOGRAPHY 64.1-2 (2012): 17–31. Print.