The geometry of covering codes: small complete caps and saturating sets in Galois spaces

被引：0

作者：

Giulietti, Massimo ^{[1
]}

机构：

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

来源：

SURVEYS IN COMBINATORICS 2013 | 2013年 / 409卷

关键词：

LINEAR CODES; ELLIPTIC-CURVES; PACKING PROBLEM; COMPLETE ARCS; CODING THEORY; DENSE SETS; CONSTRUCTIONS; RADIUS; FAMILIES; STATISTICS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Complete caps and saturating sets in projective Galois spaces are the geometrical counterpart of linear codes with covering radius 2. The smaller the cap/saturating set, the better the covering properties of the code. In this paper we survey the state of the art of the research on these geometrical objects, with particular emphasis on the recent developments and on the connections with algebraic curves over finite fields.

引用

页码：51 / 90

页数：40