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We provide a geometric characterization of k-dimensional 𝔽_q^m-linear sum-rank metric codes as tuples of 𝔽_q-subspaces of 𝔽_q^m^k. We then use this characterization to study one-weight codes in the sum-rank metric. This leads us to extend the family of linearized Reed-Solomon codes in order to obtain a doubly-extended version of them. We prove that these codes are still maximum sum-rank distance (MSRD) codes and, when k=2, they are one-weight, as in the Hamming-metric case. We then focus onarXiv:2112.04989v1 fatcat:lrhrfcqavfaqfayedpt6jzybma