NDLI: Blocking Sets in PG(r, q n )

Content Provider	Springer Nature Link
Author	Mazzocca, F. Polveri, O. Storme, L.
Copyright Year	2007
Abstract	Let $$\mathcal S$$ be a Desarguesian (n – 1)-spread of a hyperplane Σ of PG(rn, q). Let Ω and $${\bar B}$$ be, respectively, an (n – 2)-dimensional subspace of an element of $$\mathcal S $$ and a minimal blocking set of an ((r – 1)n + 1)-dimensional subspace of PG(rn, q) skew to Ω. Denote by K the cone with vertex Ω and base $${\bar B}$$ , and consider the point set B defined by $$B=\left(K\setminus\Sigma\right)\cup \{X\in \mathcal S\, : \, X\cap K\neq \emptyset\}$$ in the Barlotti–Cofman representation of PG(r, q n ) in PG(rn, q) associated to the (n – 1)-spread $$\mathcal S$$ . Generalizing the constructions of Mazzocca and Polverino (J Algebraic Combin, 24(1):61–81, 2006), under suitable assumptions on $${\bar B}$$ , we prove that B is a minimal blocking set in PG(r, q n ). In this way, we achieve new classes of minimal blocking sets and we find new sizes of minimal blocking sets in finite projective spaces of non-prime order. In particular, for q a power of 3, we exhibit examples of r-dimensional minimal blocking sets of size q n+2 + 1 in PG(r, q n ), 3 ≤ r ≤ 6 and n ≥ 3, and of size q 4 + 1 in PG(r, q 2), 4 ≤ r ≤ 6; actually, in the second case, these blocking sets turn out to be the union of q 3 Baer sublines through a point. Moreover, for q an even power of 3, we construct examples of minimal blocking sets of PG(4, q) of size at least q 2 + 2. From these constructions, we also get maximal partial ovoids of the hermitian variety H(4, q 2) of size q 4 + 1, for any q a power of 3.
Starting Page	97
Ending Page	113
Page Count	17
File Format	PDF
ISSN	09251022
Journal	Designs, Codes and Cryptography
Volume Number	44
Issue Number	1-3
e-ISSN	15737586
Language	English
Publisher	Springer US
Publisher Date	2007-07-26
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Blocking set Ovoid Spread Information and Communication, Circuits Discrete Mathematics in Computer Science Data Encryption Data Structures, Cryptology and Information Theory Coding and Information Theory Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Ovoidal blocking sets and maximal partial ovoids of Hermitian varieties

Small point sets of PG(n, q 3) intersecting each k-subspace in 1 mod q points

A small minimal blocking set in PG(n, p t ), spanning a (t − 1)-space, is linear

The characterisation of the smallest two fold blocking sets in PG(n, 2)

On the number of pairwise non-isomorphic minimal blocking sets in PG(2, q)

Infinite family of large complete arcs in PG(2, q n), with q odd and n > 1 odd

Blocking All Generators of Q+(2n + 1,3), n ≥ 4

Blocking Sets of Certain Line Sets Related to a Conic

Multiple Blocking Sets in PG(n, q), n > 3

Blocking Sets in PG(r, q n )

Similar Documents

Ovoidal blocking sets and maximal partial ovoids of Hermitian varieties

Small point sets of PG(n, q 3) intersecting each k-subspace in 1 mod q points

A small minimal blocking set in PG(n, p t ), spanning a (t − 1)-space, is linear

The characterisation of the smallest two fold blocking sets in PG(n, 2)

On the number of pairwise non-isomorphic minimal blocking sets in PG(2, q)

Infinite family of large complete arcs in PG(2, q n), with q odd and n > 1 odd

Blocking All Generators of Q+(2n + 1,3), n ≥ 4

Blocking Sets of Certain Line Sets Related to a Conic

Multiple Blocking Sets in PG(n, q), n > 3

Blocking Sets in PG(r, q n )