Deep Holes of Projective Reed-Solomon Codes

KAIPA, KRISHNA; Zhang, Jun; Wan, Daqing

dc.contributor.author	Zhang, Jun	en_US
dc.contributor.author	Wan, Daqing	en_US
dc.contributor.author	KAIPA, KRISHNA	en_US
dc.date.accessioned	2020-03-27T04:13:39Z
dc.date.available	2020-03-27T04:13:39Z
dc.date.issued	2020-04	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 66(4), 2392 – 2401.	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/4507
dc.identifier.uri	https://doi.org/10.1109/TIT.2019.2940962	en_US
dc.description.abstract	Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum possible length $q+1$ . 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.	en_US
dc.language.iso	en	en_US
dc.publisher	IEEE	en_US
dc.subject	Projective Reed-Solomon	en_US
dc.subject	Reed-Solomon codes	en_US
dc.subject	TOC-MAR-2020	en_US
dc.subject	2020	en_US
dc.subject	2020-MAR-WEEK4	en_US
dc.title	Deep Holes of Projective Reed-Solomon Codes	en_US
dc.type	Article	en_US
dc.contributor.department	Dept. of Mathematics	en_US
dc.identifier.sourcetitle	IEEE Transactions on Information Theory	en_US
dc.publication.originofpublisher	Foreign	en_US