On near-MDS codes and caps

被引：3

作者：

Ceria, Michela ^{[1
]}

Cossidente, Antonio ^{[2
]}

Marino, Giuseppe ^{[3
]}

Pavese, Francesco ^{[1
]}

机构：

[1] Politecn Bari, Dipartimento Meccan Matemat & Management, Via Orabona 4, I-70125 Bari, Italy

[2] Univ Basilicata, Dipartimento Matemat Informat & Econ, I-85100 Potenza, Italy

[3] Univ Napoli Federico II, Dipartimento Matemat & Applicaz Renato Caccioppol, Cupa Nuova Cintia 21, I-80126 Naples, Italy

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 03期

关键词：

Near-MDS code; Cap; Ovoid; Twisted cubic; OVOIDS; 4-SPACE; EVEN;

D O I：

10.1007/s10623-022-01141-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Several classes of near-MDS sets of PG(3, q) are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of a symplectic polar space W(3, q) or starting from the q + 1 points of a twisted cubic of PG(3, q). As a by-product two classes of complete caps of PG(4, q) of size 2q(2) - q +/- root 2q + 2 are exhibited.

引用

页码：1095 / 1110

页数：16

共 18 条

[1] On near–MDS codes and caps
Michela Ceria
Antonio Cossidente
Giuseppe Marino
Francesco Pavese
Designs, Codes and Cryptography, 2023, 91 : 1095 - 1110
[2] Near-MDS codes from elliptic curves
Angela Aguglia
Luca Giuzzi
Angelo Sonnino
Designs, Codes and Cryptography, 2021, 89 : 965 - 972
[3] Near-MDS codes from elliptic curves
Aguglia, Angela
Giuzzi, Luca
Sonnino, Angelo
DESIGNS CODES AND CRYPTOGRAPHY, 2021, 89 (05) : 965 - 972
[4] Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes
Fu, Qiang
Wang, Buhong
Li, Ruihu
Yang, Ruipan
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2023, E106A (08) : 1051 - 1056
[5] Near MDS codes from oval polynomials
Wang, Qiuyan
Heng, Ziling
DISCRETE MATHEMATICS, 2021, 344 (04)
[6] Near MDS Codes with Dimension 4 and Their Application in Locally Recoverable Codes
Heng, Ziling
Li, Xiaoru
ARITHMETIC OF FINITE FIELDS, WAIFI 2022, 2023, 13638 : 142 - 158
[7] Constructions of near MDS codes which are optimal locally recoverable codes
Li, Xiaoru
Heng, Ziling
FINITE FIELDS AND THEIR APPLICATIONS, 2023, 88
[8] Several Constructions of Near MDS Codes and Optimal Locally Recoverable Codes
Wang X.-R.
Heng Z.-L.
Tien Tzu Hsueh Pao/Acta Electronica Sinica, 2024, 52 (03): : 957 - 966
[9] Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of Fq2*
Heng, Ziling
Li, Chengju
Wang, Xinran
IEEE TRANSACTIONS ON INFORMATION THEORY, 2022, 68 (12) : 7817 - 7831
[10] Infinite Families of Near MDS Codes Holding t-Designs
Ding, Cunsheng
Tang, Chunming
IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (09) : 5419 - 5428

← 1 2 →