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A New Family of MRD Codes in $\mathbb{F_q}^{2n\times2n}$ With Right and Middle Nuclei $\mathbb F_{q^n}$.
- Source :
- IEEE Transactions on Information Theory; Feb2019, Vol. 65 Issue 2, p1054-1062, 9p
- Publication Year :
- 2019
-
Abstract
- In this paper, we present a new family of maximum rank-distance (MRD) codes in $\mathbb F_{q}^{2n\times 2n}$ of minimum distance $2\leq d\leq 2n$. In particular, when $d=2n$ , we can show that the corresponding semifield is exactly a Hughes–Kleinfeld semifield. The middle and right nuclei of these MRD codes are both equal to $\mathbb F_{q^{n}}$. We also prove that the MRD codes of minimum distance $2< d< 2n$ in this family are inequivalent to all known ones. The equivalence between any two members of this new family is also determined. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICAL analysis
MATHEMATICS theorems
ALGORITHMS
X-ray diffraction
POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 134231206
- Full Text :
- https://doi.org/10.1109/TIT.2018.2853184