The equipment I am trying to control is a very cheap one I got from Amazon. They even have DIP switches you can use to change the codes sent from the remote and received by the outlets (so that two outlets acts to the same button for example).
For the reception side I am using a Raspberry Pi with a program called RFSniffer. It gives me numerical values corresponding to the bits detected by the receiver.
To check those values, I also used Piscope, a sort of oscilloscope software for Raspberry Pi. I have linked a screenshot (as remote_piscope) to the output of piscope to this post. Assuming the last bit is a stop bit, the code can be read as 0000 0000 0001 0101 0001 0001(0) which is equal in demical to the 5393 I got from RFSniffer.
I tried to upload the ReceiveDemo sketch from rc-switch to my Arduino to see the receiver's values on the Arduino but unfortunately this didn't work : the switch.available() always returns 0.
To reproduce the RF from the remote, I use the code I put earlier. When this is running, I have on piscope something very similar (attached as arduino_transmit_received_piscope) although with what I would assume is parasites (see the last 2 bits).
Looking a bit further, it seems that both signals are not transmitter using the same pulse length. This might be the reason why it's not working. I'll try to sent the pulse length on the transmitter sketch and get back.
EDIT : I checked the total duration of each message : From the remote, a message seems to be 31765 µs. By default, rc-switch gave me a message of 34489 µs. I started using setPulseWidth to try to get closer to the expected duration. With setPulseWidth(321), I end up with 31656 µs and with setPulseWidth(322), I have 31776. When I use setPulseWidth, the parasites we can see on the second screenshot seem to disappear (or at least they can't be seen on piscope).

