COVERING RADIUS OF MATRIX CODES ENDOWED WITH THE RANK METRIC

被引：16
|
作者：
Byrne, Eimear [1 ]
Ravagnani, Alberto [2 ]
机构：
[1] Univ Coll Dublin, Sch Math & Stat, Dublin, Ireland
[2] Univ Toronto, Dept Elect & Comp Engn, Toronto, ON M5S 3G4, Canada
来源：
SIAM JOURNAL ON DISCRETE MATHEMATICS | 2017年 / 31卷 / 02期
基金：
瑞士国家科学基金会;
关键词：
rank-metric code; matrix code; covering radius; weight distribution;
D O I：
10.1137/16M1091769
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study properties and invariants of matrix codes endowed with the rank metric and relate them to the covering radius. We introduce new tools for the analysis of rank-metric codes, such as puncturing and shortening constructions. We give upper bounds on the covering radius of a code by applying different combinatorial methods. The various bounds are then applied to the classes of maximal-rank-distance and quasi-maximal-rank-distance codes.
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页码：927 / 944
页数：18
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