New Inductive Constructions of Complete Caps in PG(N, q), q even

被引：20

作者：

Davydov, Alexander A. ^{[1
]}

Giulietti, Massimo ^{[2
]}

Marcugini, Stefano ^{[2
]}

Pambianco, Fernanda ^{[2
]}

机构：

[1] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 127994, Russia

[2] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2010年 / 18卷 / 03期

关键词：

projective space; complete cap; complete arc; FINITE PROJECTIVE SPACES; PACKING PROBLEM; CODING THEORY; LINEAR CODES; STATISTICS; PLANES; ARCS;

D O I：

10.1002/jcd.20230

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Some new families of small complete caps in PG(N, q), q even, are described. By using inductive arguments, the problem of the construction of small complete caps in projective spaces of arbitrary dimensions is reduced to the same problem in the plane. The caps constructed in this article provide an improvement on the currently known upper bounds on the size of the smallest complete cap in PG(N, q), N >= 4, for all q >= 2(3). In particular, substantial improvements are obtained for infinite values of q square, including q =2(2Cm), C >= 5, m >= 3; for q=2(Cm), C >= 5, m >= 9, with C, m odd; and for all q <= 2(18). (C) 2009 Wiley Periodicals. Inc. J Combin Designs 18: 177-201, 2010

引用

页码：177 / 201

页数：25

共 50 条

[31] Ovoids of PG(3, q), q even, with a conic section
Brown, MR
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 62 : 569 - 582
[32] A CONDITION FOR THE EXISTENCE OF OVALS IN PG(2,Q), Q EVEN
GLYNN, DG
GEOMETRIAE DEDICATA, 1989, 32 (02) : 247 - 252
[33] On the largest caps contained in the Klein quadric of PG(5, q), q odd
Storme, L
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1999, 87 (02) : 357 - 378
[34] Eggs in PG(4n-1,q), q even, containing a pseudo-conic
Brown, MR
Lavrauw, M
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2004, 36 : 633 - 639
[35] MDS CODES AND ARCS IN PG(N,Q) WITH Q EVEN - AN IMPROVEMENT OF THE BOUNDS OF BRUEN, THAS, AND BLOKHUIS
STORME, L
THAS, JA
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1993, 62 (01) : 139 - 154
[36] A new lower bound for the smallest complete (k,n)-arc in PG(2,q)
Alabdullah, S.
Hirschfeld, J. W. P.
DESIGNS CODES AND CRYPTOGRAPHY, 2019, 87 (2-3) : 679 - 683
[37] Proper 2-covers of PG(3,q), q even
Drudge, K
GEOMETRIAE DEDICATA, 2000, 80 (1-3) : 59 - 64
[38] MAXIMAL PARTIAL LINE SPREADS OF PG(3,q), q EVEN
Tallini, Maria Scafati
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2012, (29): : 333 - 340
[39] Proper 2-Covers of PG(3,q), q Even
Keldon Drudge
Geometriae Dedicata, 2000, 80 : 59 - 64
[40] A characterization of the external lines of a hyperoval in PG(3, q), q even
Zuanni, Fulvio
DISCRETE MATHEMATICS, 2012, 312 (06) : 1257 - 1259

← 1 2 3 4 5 →