Let C be a (n, q 2k , n − k + 1) q 2 additive MDS code which is linear over F q . We prove that if n q + k and k + 1 of the projections of C are linear over F q 2 then C is linear over F q 2 . We use this geometrical theorem, other geometric arguments and some computations to classify all additive MDS codes over F q for q ∈ {4, 8, 9}. We also classify the longest additive MDS codes over F 16 which are linear over F 4 . In these cases, the classifications not only verify the MDS conjecture for additive codes, but also confirm there are no additive non-linear MDS codes which perform as well as their linear counterparts. These results imply that the quantum MDS conjecture holds for q ∈ {2, 3}.
In this work we studied the influence of the microwave irradiation in polar Diels-Alder reactions using nitropyrrole and nitroindole derivatives as electrophiles with dienes of different nucleophilicity. The cycloadditions was performed under two conditions with benzene as the reaction medium and solvent free. The results clearly confirm that the use of microwave irradiation in this type of reactions have advantages in relation to the carried out under classical heating. In general the products obtained are similar, but reaction times are lower and the yields increases.
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