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New full-diversity STBCs with low ML decoding complexity and cubic shaping property are constructed, via codes over $\\mathbb{F}_4$, for number of transmit antennas \\mbox{$N=2^m$}, \\mbox{$m \\geq 1$}, and rates \\mbox{$R>1$} complex symbols per channel use. When \\mbox{$R=N$}, the new STBCs are information-lossless as well. 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