Reed–solomon codes over small fields with constrained generator matrices

Reed–solomon codes over small fields with constrained generator matrices

We give constructions of some special cases of [n, k] Reed-Solomon codes over finite fields of size at least n and n + 1 whose generator matrices have constrained support. Furthermore, we consider a generalization of the GM-MDS conjecture proposed by Lovett in 2018. We show that Lovett's conjec...

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Main Authors: Greaves, Gary, Syatriadi, Jeven
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2020
Subjects:
Science::Mathematics
Reed-Solomon Codes
Small Fields
Online Access:https://hdl.handle.net/10356/143861
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1438612023-02-28T19:47:58Z Reed–solomon codes over small fields with constrained generator matrices Greaves, Gary Syatriadi, Jeven School of Physical and Mathematical Sciences Science::Mathematics Reed-Solomon Codes Small Fields We give constructions of some special cases of [n, k] Reed-Solomon codes over finite fields of size at least n and n + 1 whose generator matrices have constrained support. Furthermore, we consider a generalization of the GM-MDS conjecture proposed by Lovett in 2018. We show that Lovett's conjecture is false in general and we specify when the conjecture is true. Ministry of Education (MOE) Accepted version G.G. was supported by the Singapore Ministry of Education AcademicResearch Fund(Tier 1); grant number: RG127/16. 2020-09-28T04:02:56Z 2020-09-28T04:02:56Z 2019 Journal Article Greaves, G., & Syatriadi, J. (2019). Reed–Solomon Codes Over Small Fields With Constrained Generator Matrices. IEEE Transactions on Information Theory, 65(8), 4764–4770. doi:10.1109/tit.2019.2897767 0018-9448 https://hdl.handle.net/10356/143861 10.1109/TIT.2019.2897767 8 65 4764 4770 en IEEE Transactions on Information Theory © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: https://doi.org/10.1109/TIT.2019.2897767. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Reed-Solomon Codes
Small Fields
spellingShingle Science::Mathematics
Reed-Solomon Codes
Small Fields
Greaves, Gary
Syatriadi, Jeven
Reed–solomon codes over small fields with constrained generator matrices
description We give constructions of some special cases of [n, k] Reed-Solomon codes over finite fields of size at least n and n + 1 whose generator matrices have constrained support. Furthermore, we consider a generalization of the GM-MDS conjecture proposed by Lovett in 2018. We show that Lovett's conjecture is false in general and we specify when the conjecture is true.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Greaves, Gary
Syatriadi, Jeven
format Article
author Greaves, Gary
Syatriadi, Jeven
author_sort Greaves, Gary
title Reed–solomon codes over small fields with constrained generator matrices
title_short Reed–solomon codes over small fields with constrained generator matrices
title_full Reed–solomon codes over small fields with constrained generator matrices
title_fullStr Reed–solomon codes over small fields with constrained generator matrices
title_full_unstemmed Reed–solomon codes over small fields with constrained generator matrices
title_sort reed–solomon codes over small fields with constrained generator matrices
publishDate 2020
url https://hdl.handle.net/10356/143861
_version_ 1759854201724207104

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