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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/143861 |
| _version_ | 1826114900157530112 |
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| author | Greaves, Gary Syatriadi, Jeven |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Greaves, Gary Syatriadi, Jeven |
| author_sort | Greaves, Gary |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T03:46:45Z |
| format | Journal Article |
| id | ntu-10356/143861 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:46:45Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-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 |
| spellingShingle | Science::Mathematics Reed-Solomon Codes Small Fields Greaves, Gary Syatriadi, Jeven Reed–solomon codes over small fields with constrained generator matrices |
| title | 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_short | Reed–solomon codes over small fields with constrained generator matrices |
| title_sort | reed solomon codes over small fields with constrained generator matrices |
| topic | Science::Mathematics Reed-Solomon Codes Small Fields |
| url | https://hdl.handle.net/10356/143861 |
| work_keys_str_mv | AT greavesgary reedsolomoncodesoversmallfieldswithconstrainedgeneratormatrices AT syatriadijeven reedsolomoncodesoversmallfieldswithconstrainedgeneratormatrices |