As far as taking-away of the symmetry constraints is concerned, as a scientifically symmetry problem, the global synthesis for antenna arrays that produce the desired radiation pattern is also a highly nonlinear optimization issue in fact. Besides this, the built criteria offer the reasonable power patterns. The consequent synthesis could be implemented by looking for a nominal pattern. When the criteria are already sufficient, it can simply do the whole synthesis process. To utilize multiple antennae, a method to choose a transmit antenna for the linear dispersion codes (LDC-TAS) is implemented in this paper. The authors used the max-min-post- signal to noise ratio (SNR) criteria to select these optimal transmitting antennae while this dependent, linear receiver is applied to the varying and slow channel. The simulated results illustrate that this max-min-post-SNR criterion outperforms the Bell Labs layered space time transmitting antenna selection (BLAST-TAS) applying the same spectral efficiency than space-time block codes (STBC)-TAS in the environment with low SNR. Furthermore, once the M antennae are selected under the selection criteria, a max-min-post-SNR rule, a novel linear antenna synthesis to linear dispersion codes on the basis of an innovative HYBRID (of mixed characters or solutions) genetic algorithm has been presented and evaluated to formulate and address the optimal problem to non-uniformly spaced and linear arrays. The restricted side-lobes level, the main-lobe width, and the shaped beam pattern are contemporarily concerned via maximizing a pretty suitable cost function through the innovational advanced genetic-algorithm-based algorithm. The method proposed in this paper can provide flexibility and a simple insertion of the a priori knowledge under a small computing pressure. At last, a computing simulation is completed well and the results are shown. It should be noticed that some extensions of the presented method could also be easily utilized without an obvious increase in the algorithm complexity.