A GEOMETRIC CHARACTERIZATION OF MINIMAL CODES AND THEIR ASYMPTOTIC PERFORMANCE

被引：35

作者：

Alfarano, Gianira N. ^{[1
]}

Borello, Martino ^{[2
]}

Neri, Alessandro ^{[3
]}

机构：

[1] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

[2] Univ Sorbonne Paris Nord, Univ Paris 08, Lab Geometrie Anal & Applicat, LAGA,CNRS,UMR 7539, F-93430 Villetaneuse, France

[3] Tech Univ Munich, Inst Commun Engn, Theresienstr 90, D-80333 Munich, Germany

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2022年 / 16卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

Minimal codes; cutting blocking sets; asymptotically good codes; projective systems; secrete sharing schemes; LINEAR CODES;

D O I：

10.3934/amc.2020104

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we give a geometric characterization of minimal linear codes. In particular, we relate minimal linear codes to cutting blocking sets, introduced in a recent paper by Bonini and Borello. Using this characterization, we derive some bounds on the length and the distance of minimal codes, according to their dimension and the underlying field size. Furthermore, we show that the family of minimal codes is asymptotically good. Finally, we provide some geometrical constructions of minimal codes as cutting blocking sets.

引用

页码：115 / 133

页数：19

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