Deep Holes of Twisted Reed-Solomon Codes

被引：2
作者：
Fang, Weijun [1 ]
Xu, Jingke [2 ]
机构：
[1] Shandong Univ, Sch Cyber Sci & Technol, Qingdao, Peoples R China
[2] Shandong Agr Univ, Sch Informat Sci & Engn, Tai An, Shandong, Peoples R China
来源：
2024 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, ISIT 2024 | 2024年
基金：
中国国家自然科学基金;
关键词：
COVERING RADIUS; MDS EXTENSIONS;
D O I：
10.1109/ISIT57864.2024.10619676
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The deep holes of a linear code are the vectors achieving maximum error distance to the code. There has been a lot of work on the deep holes of Reed-Solomon codes. In this paper, we consider the deep holes of a class of twisted Reed-Solomon codes. The covering radius and a standard class of deep holes of twisted Reed-Solomon codes TRSk(A, eta) are obtained for a general evaluation set A subset of F-q. Furthermore, when q = 2(m) >= 8, we prove that there are no other deep holes of the full-length twisted Reed-Solomon codes TRSk(F-q, eta) for 3/4 q - 1 <= k q - 4, and we also completely determine their deep holes for q - 3 <= k <= q - 1.
引用
收藏
页码：488 / 493
页数：6
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