SHORT RANK-METRIC CODES AND SCATTERED SUBSPACES

被引：0

作者：

Lia, Stefano ^{[1
]}

Longobardi, Giovanni

Marino, Giuseppe ^{[2
]}

Trombetti, Rocco ^{[2
]}

机构：

[1] Univ Coll Dublin, Sch Math & Stat, Dublin, Ireland

[2] Univ Naples Federico II, Dept Math & Applicat Renato Caccioppoli, Via Cintia, I-80126 Naples, Italy

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2024年 / 38卷 / 04期

关键词：

scattered subspaces; linear sets; cutting blocking sets; rank-metric codes; POLYNOMIALS; FIELD;

D O I：

10.1137/23M1574749

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By exploiting the connection between scattered F-q-subspaces of F-qm(3) and minimal nondegenerate 3-dimensional rank-metric codes of F-qm(n), n >= m + 2, described in [G. N. Alfarano et al., J. Combin. Theory Ser. A, 192 (2022), 105658], we will exhibit a new class of codes with parameters [m+ 2, 3, m 2](qm/q) for infinite values of q and m >= 5 odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.

引用

页码：2578 / 2598

页数：21

共 50 条

[31] Constructions for Optimal Ferrers Diagram Rank-Metric Codes
Liu, Shuangqing
Chang, Yanxun
Feng, Tao
IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (07) : 4115 - 4130
[32] q-polymatroids and their relation to rank-metric codes
Gluesing-Luerssen, Heide
Jany, Benjamin
JOURNAL OF ALGEBRAIC COMBINATORICS, 2022, 56 (03) : 725 - 753
[33] RANK-METRIC CODES, SEMIFIELDS, AND THE AVERAGE CRITICAL PROBLEM
Gruica, A. N. I. N. A.
Ravagnani, A. L. B. E. R. T. O.
Sheekey, J. O. H. N.
Zullo, F. E. R. D. I. N. A. N. D. O.
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2023, 37 (02) : 1079 - 1117
[34] Higher-Degree Symmetric Rank-Metric Codes
Bik, Arthur
Neri, Alessandro
SIAM Journal on Applied Algebra and Geometry, 2024, 8 (04) : 931 - 967
[35] q-polymatroids and their relation to rank-metric codes
Heide Gluesing-Luerssen
Benjamin Jany
Journal of Algebraic Combinatorics, 2022, 56 : 725 - 753
[36] Space-Time Codes Based on Rank-Metric Codes and Their Decoding
Puchinger, Sven
Stern, Sebastian
Bossert, Martin
Fischer, Robert F. H.
2016 13TH INTERNATIONAL SYMPOSIUM ON WIRELESS COMMUNICATION SYSTEMS (ISWCS), 2016, : 125 - 130
[37] Optimal Ferrers diagram rank-metric codes from MRD codes
Liu, Shuangqing
DESIGNS CODES AND CRYPTOGRAPHY, 2023, 91 (12) : 3977 - 3993
[38] Equivalence for Rank-Metric and Matrix Codes and Automorphism Groups of Gabidulin Codes
Morrison, Katherine
IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (11) : 7035 - 7046
[39] Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions
Byrne, Eimear
Cotardo, Giuseppe
Ravagnani, Alberto
LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 604 : 92 - 128
[40] On the List-Decodability of Random Linear Rank-Metric Codes
Guruswami, Venkatesan
Resch, Nicolas
2018 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2018, : 1505 - 1509

← 1 2 3 4 5 →