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On the minimum number of points covered by a set of lines in P G (2, q)
- Authors
- Cheon, Eun Ju; Kim, Seon Jeong
- Issue Date
- Jan-2015
- Publisher
- SPRINGER
- Keywords
- Projective plane; Rational point; Arc; Hyperoval; Conic; Largest arc
- Citation
- DESIGNS CODES AND CRYPTOGRAPHY, v.74, no.1, pp 59 - 74
- Pages
- 16
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- DESIGNS CODES AND CRYPTOGRAPHY
- Volume
- 74
- Number
- 1
- Start Page
- 59
- End Page
- 74
- ISSN
- 0925-1022
1573-7586
- Abstract
- Segre (Ann Mat Pura Appl 48:1-96, 1959) mentioned that the number of points on a curve which splits into distinct lines on the projective plane over a finite field of order satisfies We see that the upper bound is satisfactory, but the lower one is not for [resp. ] if is odd [resp. even]. We consider the minimum number of points on such a curve of degree , and obtain the complete sequence for every prime power q <= 8.
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