For precise start time determination a Beam Fragmentation T$_0$ Counter (BFTC) is under development for the Time-of-Flight Wall of the Compressed Baryonic Matter Spectrometer (CBM) at the Facility for Antiproton and Ion Research (FAIR) at Darmstadt/Germany. This detector will be located around the beam pipe, covering the front area of the Projectile Spectator Detector. The fluxes at this region are expected to exceed 10$^5$cm$^{-2}$s$^{-1}$. Resistive plate chambers (RPC) with ceramic composite electrodes could be use because of their high rate capabilities and radiation hardness of material. Efficiency $ge$ 97%, time resolution $le$ 90 ps and rate capability $ge$ 10$^5$cm$^{-2}$s$^{-1}$ were confirmed during many tests with high beam fluxes of relativistic electrons. We confirm the stability of these characteristics with low resistive Si$_3$N$_4$/SiC floating electrodes for a prototype of eight small RPCs, where each of them contains six gas gaps. The active RPC size amounts 20$times$20 mm$^2$ produced on basis of Al$_3$O$_2$ and Si$_3$N$_4$/SiC ceramics. Recent test results obtained with relativistic electrons at the linear accelerator ELBE of the Helmholtz-Zentrum Dresden-Rossendorf with new PADI-10 Front-end electronic will be presented.
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