MDS and near-MDS codes via twisted Reed–Solomon codes

被引：0
作者：
Junzhen Sui
Xiaomeng Zhu
Xueying Shi
机构：
[1] Nanjing University of Aeronautics and Astronautics,College of Computer Science and Technology
[2] Nanjing University of Aeronautics and Astronautics,Department of Mathematics
[3] Taizhou University,Department of Mathematics
来源：
Designs, Codes and Cryptography | 2022年 / 90卷
关键词：
MDS codes; NMDS codes; Twisted Reed–Solomon codes; 94B05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for a given length and code size. Twisted Reed–Solomon codes come from Reed–Solomon codes by adding a monomial. In this paper, we give a necessary and sufficient condition that twisted Reed–Solomon codes are MDS (near-MDS). Moreover, we prove that a lot of MDS codes, which are constructed via twisted Reed–Solomon codes, are not equivalent to Reed–Solomon codes.
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页码：1937 / 1958
页数：21
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