Reed–Solomon Codes Over Small Fields With Constrained Generator Matrices
| Autor: | Gary R. W. Greaves, Jeven Syatriadi |
|---|---|
| Přispěvatelé: | School of Physical and Mathematical Sciences |
| Rok vydání: | 2019 |
| Předmět: |
Mathematics [Science]
Discrete mathematics Conjecture Generalization 020206 networking & telecommunications Data_CODINGANDINFORMATIONTHEORY 02 engineering and technology Library and Information Sciences Computer Science Applications Finite field Reed–Solomon error correction Small Fields 0202 electrical engineering electronic engineering information engineering Generator matrix Reed-Solomon Codes Computer Science::Information Theory Information Systems Mathematics |
| Zdroj: | IEEE Transactions on Information Theory. 65:4764-4770 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2019.2897767 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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