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

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