MO3.R7.3

Deep Holes of Twisted Reed-Solomon Codes

Weijun Fang, Shandong University, China; Jingke Xu, Shandong Agricultural University, China
Session:
Reed Solomon Codes
Track:
1: Algebraic Aspects of Coding Theory
Location:
VIP
Presentation Time:
Mon, 8 Jul, 15:15 - 15:35
Session Chair:
Eduardo Camps, Virginia Tech
Abstract
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 ${\rm TRS}_k(A, \eta)$ are obtained for a general evaluation set $A \subseteq \mathbb{F}_q$. Furthermore, when $q=2^m \geq 8$, we prove that there are no other deep holes of the full-length twisted Reed-Solomon codes ${\rm TRS}_k(\mathbb{F}_q, \eta)$ for $\frac{3q-8}{4} \leq k\leq q-4$, and we also completely determine their deep holes for $q-3 \leq k \leq q-1$.
Session MO3.R7
MO3.R7.1: Efficient Decoding of a Class of Reed-Solomon Codes over Fermat Fields
Chao Chen, Baoming Bai, Xidian University, China; Xiao Ma, Sun Yat-sen University, China; Yunghsiang S Han, Nianqi Tang, University of Electronic Science and Technology of China, China; Xiaotian Wang, Xidian University, China
MO3.R7.2: Reed-Solomon Codes over Cyclic Polynomial Ring with Lower Encoding/Decoding Complexity
Wenhao Liu, Zhengyi Jiang, Zhongyi Huang, Tsinghua University, China; Linqi Song, City University of Hong Kong, China; Hanxu Hou, Dongguan University of Technology, China
MO3.R7.3: Deep Holes of Twisted Reed-Solomon Codes
Weijun Fang, Shandong University, China; Jingke Xu, Shandong Agricultural University, China
MO3.R7.4: Repairing Reed-Solomon Codes with Less Bandwidth
SHU LIU, University of Electronic Science and Technology of China, China; Yunqi Wan, Huawei Technology Co. Ltd., China; CHAOPING XING, Shanghai Jiao Tong University, China
Resources
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