MDS or NMDS LCD codes from twisted Reed-Solomon codes

被引：7
|
作者：
Huang, Daitao [1 ]
Yue, Qin [2 ]
Niu, Yongfeng [1 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Coll Comp Sci & Technol, Nanjing 211100, Peoples R China
[2] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211100, Peoples R China
来源：
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2023年 / 15卷 / 02期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
Linear complementary dual; Generalized twisted Reed-Solomon codes; MDS codes; LINEAR CODES; COMPLEMENTARY;
D O I：
10.1007/s12095-022-00564-9
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Maximum distance separable (MDS) codes are optimal with parameters [n,k,n - k + 1]. Near MDS (NMDS) codes were introduced in 1995 by weakening the definition of MDS codes. NMDS codes also have applications in secret sharing scheme. Linear complementary dual (LCD) codes have been widely used in communications systems, consumer electronics, cryptography and so on. The construction of LCD MDS codes is thus interesting in coding theory. Twisted Reed Solomon (TRS) codes are generalized by Reed Solomon (RS) codes and are not equivalent to RS codes in general case. In this paper, we give parity check matrices of twisted generalized Reed-Solomon (TGRS) codes, show the sufficient and necessary condition that TGRS codes are MDS or NMDS codes, and construct several classes of LCD MDS or NMDS codes from two classes of TGRS codes.
引用
收藏
页码：221 / 237
页数：17
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