Yes I initially sorted the output of the 555, so I have tried to put a 100nF capacitor at the output so not DC passes through. The pulse was able to pass through the capacitor and induce the waveform shown in the diagram on the secondary.
Then I ingreased the number of turns on the secondary from 10 to 30, so now the primary was 1 turn and the secondary 30 turns. I got a much greater amplitude output and the same waveform shape, as it was expected.
The load in both cases were just an oscilloscope connected at the output. I have also tried to connect a diode accross one of the secondary windings. This diode rectified the waveform and let only the top side (positive) to pass through the oscilloscope.
In a ROM configuration, core saturation is not desired, since in every prescending pulse you need to get an output. If the core has been saturated by a positive pulse, the next positive pulses would have no output effect I think.
By the way, have you got any ideas, of how could I detect if a core is saturated or not? Maybe by applying more pulses and notice if there is a waveform on the output or not?
Also, what is the saturation effect of using smaller ferrite cores, will they need less turns or power to saturate?