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
相关论文
共 50 条
  • [21] Rank-metric codes, linear sets, and their duality
    John Sheekey
    Geertrui Van de Voorde
    Designs, Codes and Cryptography, 2020, 88 : 655 - 675
  • [22] Eigenvalue bounds and alternating rank-metric codes
    Abiad, Aida
    Alfarano, Gianira N.
    Ravagnani, Alberto
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2025,
  • [23] SHORT RANK-METRIC CODES AND SCATTERED SUBSPACES
    Lia, Stefano
    Longobardi, Giovanni
    Marino, Giuseppe
    Trombetti, Rocco
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2024, 38 (04) : 2578 - 2598
  • [24] Invariants and Inequivalence of Linear Rank-Metric Codes
    Neri, Alessandro
    Puchinger, Sven
    Horlemann-Trautmann, Anna-Lena
    2019 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2019, : 2049 - 2053
  • [25] Optimal Ferrers Diagram Rank-Metric Codes
    Etzion, Tuvi
    Gorla, Elisa
    Ravagnani, Alberto
    Wachter-Zeh, Antonia
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (04) : 1616 - 1630
  • [26] On the list decodability of rank-metric codes containing Gabidulin codes
    Santonastaso, Paolo
    Zullo, Ferdinando
    DESIGNS CODES AND CRYPTOGRAPHY, 2022, 90 (04) : 957 - 982
  • [27] Rank-metric codes as ideals for subspace codes and their weight properties
    Hernandez, Bryan S.
    Sison, Virgilio P.
    AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2019, 16 (02) : 190 - 197
  • [28] Optimal Locally Repairable Codes via Rank-Metric Codes
    Silberstein, Natalia
    Rawat, Ankit Singh
    Koyluoglu, O. Ozan
    Vishwanath, Sriram
    2013 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT), 2013, : 1819 - 1823
  • [29] On the list decodability of rank-metric codes containing Gabidulin codes
    Paolo Santonastaso
    Ferdinando Zullo
    Designs, Codes and Cryptography, 2022, 90 : 957 - 982
  • [30] On Decoding Rank-Metric Codes Over Large Fields
    Roth, Ron M.
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2018, 64 (02) : 944 - 951
12345