MRD codes with maximum idealizers

Left and right idealizers are important invariants of linear rank-distance codes. In the case of maximum rank-distance (MRD for short) codes in $\mathbb{F}_q^{n\times n}$ the idealizers have been proved to be isomorphic to finite fields of size at most $q^n$. Up to now, the only known MRD codes with maximum left and right idealizers are generalized Gabidulin codes, which were first constructed in 1978 by Delsarte and later generalized by Kshevetskiy and Gabidulin in 2005. In this paper we classify MRD codes in $\mathbb{F}_q^{n\times n}$ for $n\leq 9$ with maximum left and right idealizers and connect them to Moore-type matrices. Apart from generalized Gabidulin codes, it turns out that there is a further family of rank-distance codes providing MRD ones with maximum idealizers for $n=7$, $q$ odd and for $n=8$, $q\equiv 1 \pmod 3$. These codes are not equivalent to any previously known MRD code. Moreover, we show that this family of rank-distance codes does not provide any further examples for $n\geq 9$.Comment: Reviewers' comments implemented, we changed the titl

Oil and Cocoa in the Political Economy of Ghana-EU Relations: Whither Sustainable Development?

Oil and cocoa represent strategic export commodities for the Ghanaian economy, prioritised within the Ghana Shared Growth and Development Agenda. This article examines these sectors in the context of Ghana’s relations with the European Union (EU). Notably, the EU constitutes the most important market for Ghanaian exports. The European Commission, moreover, has pledged to tangibly assist private sector development in Ghana, with particular reference to the UN Sustainable Development Goals (SDGs). Through its focus on oil and cocoa, the article problematises certain aspects of EU aid and trade interventions with respect to normative SDG development pledges

Thymidylate kinase of Mycobacterium tuberculosis: A chimera sharing properties common to eukaryotic and bacterial enzymes

We have overexpressed in Escherichia coli the thymidylate kinase of Mycobacterium tuberculosis (TMPKmt). Biochemical and physico-chemical characterization of TMPKmt revealed distinct structural and catalytic features when compared to its counterpart from yeast (TMPKy) or E. coli (TMPKec). Denaturation of the dimeric TMPKmt by urea under equilibrium conditions was studied by intrinsic fluorescence and circular dichroism (CD) spectroscopy. It suggested a three-state unfolding mechanism with a monomeric intermediate. On the other hand, 3′-azido-3′-deoxythymidine monophosphate (AZT-MP), which is substrate for TMPKy and TMPKec acts as a potent competitive inhibitor for TMPKmt. We propose a structural model of TMPKmt in which the overall fold described in TMPKy and TMPKec is conserved and slight differences at the level of primary and 3D-structure explain strong variations in the phosphorylation rate of substrate analogs. According to the model, we synthesized dTMP analogs acting either as substrates or specific inhibitors of TMPKmt. This approach based on slight structural differences among similar proteins could be applied to other essential enzymes for the design of new species-specific antimicrobials