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The authors investigate the design of linear dispersion (LD) codes, aiming at flexible encoding schemes that allow various rate-performance tradeoffs under a common coding structure. First, the capacity of LD codes is studied. It is shown that the maximum attainable multiplexing gain of a linear dispersion code is the number of symbols per channel use of the code (i.e. coding rate in symbols). In addition, conditions on the construction of linear dispersion matrices for various multiplexing gains are established. A general multilayered linear dispersion coding scheme that allows various multiplexing gains is then proposed. In the proposed scheme, coding rate can be adapted by employing different numbers of dispersion matrices. Furthermore, phase shifting among input symbols is applied to optimise the error performance without loss of multiplexing gain. The construction of dispersion matrices and the optimisation of the phase shifts together constitute a structured approach for the design of linear dispersion codes. Simulation results demonstrate that the new codes outperform conventional LD codes at various data rates.