New constructions of self-dual generalized reed-solomon codes

被引:9
作者
Fang, Weijun [1 ]
Zhang, Jun [2 ]
Xia, Shu-Tao [3 ]
Fu, Fang-Wei [4 ,5 ]
机构
[1] Shandong Univ, Sch Cyber Sci & Technol, Qingdao 266237, Peoples R China
[2] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[3] Tsinghua Univ, Shenzhen Int Grad Sch, Shenzhen 518055, Peoples R China
[4] Nankai Univ, Chern Inst Math & LPMC, Tianjin 300071, Peoples R China
[5] Nankai Univ, Tianjin Key Lab Network & Data Secur Technol, Tianjin 300071, Peoples R China
来源
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2022年 / 14卷 / 03期
基金
中国国家自然科学基金; 中国博士后科学基金;
关键词
MDS codes; Self-dual codes; Generalized reed-solomon codes; Mobius action; MDS;
D O I
10.1007/s12095-021-00549-0
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider new constructions of MDS self-dual codes via generalized Reed-Solomon (GRS) codes and their extended codes. The critical idea of our constructions is to choose suitable evaluation points such that the corresponding (extended) GRS codes are self-dual. The evaluation set of our constructions consists of a subgroup of finite fields and its cosets in a bigger subgroup. Four new families of MDS self-dual codes are then obtained. Moreover, by the Mobius action over finite fields, for any known self-dual GRS codes, we give a systematic way to construct new self-dual GRS codes with flexible evaluation points.
引用
收藏
页码:677 / 690
页数:14
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