Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions

被引：7
|
作者：
Byrne, Eimear [1 ]
Cotardo, Giuseppe [1 ]
Ravagnani, Alberto [2 ]
机构：
[1] Univ Coll Dublin, Sch Math & Stat, Dublin, Ireland
[2] Eindhoven Univ Technol, Dept Math & Comp Sci, Eindhoven, Netherlands
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 604卷
关键词：
Rank-metric code; Zeta function; Binomial moments; Generalized rank weights; Generalized rank weight distribution;
D O I：
10.1016/j.laa.2020.06.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we introduce a new class of extremal codes, namely the i-BMD codes. We show that for this family several of the invariants are determined by the parameters of the underlying code. We refine and extend the notion of an i-MRD code and show that the i-BMD codes form a proper subclass of the i-MRD codes. Using the class of i-BMD codes we then obtain a relation between the generalized rank weight enumerator and its corresponding generalized zeta function. We also establish a MacWilliams identity for generalized rank weight distributions. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码：92 / 128
页数：37
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