On the cardinality of blocking sets in PG(2,q)

Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Berardi, Luigia [verfasserIn] Eugeni, Franco

Format:	Artikel
Sprache:	Englisch

Erschienen:	1984

Schlagwörter:	Projective Plane Desarguesian Projective Plane Great Divisor Finite Desarguesian Projective Plane

Anmerkung:	© Birkhäuser Verlag 1984

Übergeordnetes Werk:	Enthalten in: Journal of geometry - Birkhäuser-Verlag, 1971, 22(1984), 1 vom: März, Seite 5-14
Übergeordnetes Werk:	volume:22 ; year:1984 ; number:1 ; month:03 ; pages:5-14

Links:	Volltext

DOI / URN:	10.1007/BF01230120

Katalog-ID:	OLC2069413144

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520			\|a Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements.
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allfields	10.1007/BF01230120 doi (DE-627)OLC2069413144 (DE-He213)BF01230120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berardi, Luigia verfasserin aut On the cardinality of blocking sets in PG(2,q) 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1984 Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. Projective Plane Desarguesian Projective Plane Great Divisor Finite Desarguesian Projective Plane Eugeni, Franco aut Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 22(1984), 1 vom: März, Seite 5-14 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:22 year:1984 number:1 month:03 pages:5-14 https://doi.org/10.1007/BF01230120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 22 1984 1 03 5-14
spelling	10.1007/BF01230120 doi (DE-627)OLC2069413144 (DE-He213)BF01230120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berardi, Luigia verfasserin aut On the cardinality of blocking sets in PG(2,q) 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1984 Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. Projective Plane Desarguesian Projective Plane Great Divisor Finite Desarguesian Projective Plane Eugeni, Franco aut Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 22(1984), 1 vom: März, Seite 5-14 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:22 year:1984 number:1 month:03 pages:5-14 https://doi.org/10.1007/BF01230120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 22 1984 1 03 5-14
allfields_unstemmed	10.1007/BF01230120 doi (DE-627)OLC2069413144 (DE-He213)BF01230120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berardi, Luigia verfasserin aut On the cardinality of blocking sets in PG(2,q) 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1984 Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. Projective Plane Desarguesian Projective Plane Great Divisor Finite Desarguesian Projective Plane Eugeni, Franco aut Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 22(1984), 1 vom: März, Seite 5-14 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:22 year:1984 number:1 month:03 pages:5-14 https://doi.org/10.1007/BF01230120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 22 1984 1 03 5-14
allfieldsGer	10.1007/BF01230120 doi (DE-627)OLC2069413144 (DE-He213)BF01230120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berardi, Luigia verfasserin aut On the cardinality of blocking sets in PG(2,q) 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1984 Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. Projective Plane Desarguesian Projective Plane Great Divisor Finite Desarguesian Projective Plane Eugeni, Franco aut Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 22(1984), 1 vom: März, Seite 5-14 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:22 year:1984 number:1 month:03 pages:5-14 https://doi.org/10.1007/BF01230120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 22 1984 1 03 5-14
allfieldsSound	10.1007/BF01230120 doi (DE-627)OLC2069413144 (DE-He213)BF01230120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berardi, Luigia verfasserin aut On the cardinality of blocking sets in PG(2,q) 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1984 Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. Projective Plane Desarguesian Projective Plane Great Divisor Finite Desarguesian Projective Plane Eugeni, Franco aut Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 22(1984), 1 vom: März, Seite 5-14 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:22 year:1984 number:1 month:03 pages:5-14 https://doi.org/10.1007/BF01230120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 22 1984 1 03 5-14
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source	Enthalten in Journal of geometry 22(1984), 1 vom: März, Seite 5-14 volume:22 year:1984 number:1 month:03 pages:5-14
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topic_title	510 VZ 17,1 ssgn On the cardinality of blocking sets in PG(2,q) Projective Plane Desarguesian Projective Plane Great Divisor Finite Desarguesian Projective Plane
topic	ddc 510 ssgn 17,1 misc Projective Plane misc Desarguesian Projective Plane misc Great Divisor misc Finite Desarguesian Projective Plane
topic_unstemmed	ddc 510 ssgn 17,1 misc Projective Plane misc Desarguesian Projective Plane misc Great Divisor misc Finite Desarguesian Projective Plane
topic_browse	ddc 510 ssgn 17,1 misc Projective Plane misc Desarguesian Projective Plane misc Great Divisor misc Finite Desarguesian Projective Plane
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title	On the cardinality of blocking sets in PG(2,q)
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title_full	On the cardinality of blocking sets in PG(2,q)
author_sort	Berardi, Luigia
journal	Journal of geometry
journalStr	Journal of geometry
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author_browse	Berardi, Luigia Eugeni, Franco
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doi_str_mv	10.1007/BF01230120
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title_sort	on the cardinality of blocking sets in pg(2,q)
title_auth	On the cardinality of blocking sets in PG(2,q)
abstract	Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. © Birkhäuser Verlag 1984
abstractGer	Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. © Birkhäuser Verlag 1984
abstract_unstemmed	Abstract Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=$ p^{h} $, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=$ p^{h−d} $, if q=$ p^{h} $ with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ $ q^{2} $−m(q), there exists a blocking set in PG(2,q) having exactly k elements. © Birkhäuser Verlag 1984
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container_issue	1
title_short	On the cardinality of blocking sets in PG(2,q)
url	https://doi.org/10.1007/BF01230120
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up_date	2024-07-03T22:07:02.494Z
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