Title
Deep Holes of Projective Reed-Solomon Codes
Abstract
Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum possible length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q+1$ </tex-math></inline-formula> . The classification of deep holes –received words with maximum possible error distance– for PRS codes is an important and difficult problem. In this paper, we use algebraic methods to explicitly construct three classes of deep holes for PRS codes. We show that these three classes completely classify all deep holes of PRS codes with redundancy four. Previously, the deep hole classification was only known for PRS codes with redundancy at most three.
Year
DOI
Venue
2020
10.1109/TIT.2019.2940962
IEEE Transactions on Information Theory
Keywords
DocType
Volume
Reed-Solomon codes,Linear codes,Measurement,Parity check codes,Gold,Redundancy,Education
Journal
66
Issue
ISSN
Citations 
4
0018-9448
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Jun Zhang131.09
Daqing Wan215223.51
Krishna V. Kaipa3153.32