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arXiv · 1709.03908

A new family of MRD codes in $\mathbb F_q^{2n\times2n}$ with right and middle nuclei $\mathbb F_{q^n}$

Rocco Trombetti·Yue Zhou
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Abstract

In this paper, we present a new family of maximum rank distance (MRD for short) 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.

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Rocco Trombetti, Yue Zhou. 2017-09-12. A new family of MRD codes in $\mathbb F_q^{2n\times2n}$ with right and middle nuclei $\mathbb F_{q^n}$. https://doi.org/10.1109/tit.2018.2853184

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