Typical linearly tapered slot antenna (LTSA) usually features a wideband and a high gain. However, its geometry size is large, especially very long in the tapering direction, which limits its application in compact antenna and array systems. This communication has minimized the tapered length to less than 0.19 lambda(0) when the aperture width is less than 0.35 lambda(0) both for horizontally and vertically polarized LTSA arrays. Moreover, the typical polarization of the LTSA is linear, which is perpendicular to the slot. In this communication, an X-band circularly polarized 1x8 LTSA array, made of cross-LTSAs, is proposed with the feeding of a substrate integrated waveguide horn. All the three different polarized LTSA arrays are designed and investigated both in simulation and experiment, and the simulation results agree well with the measured results.