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In this paper, we consider the problem of designing parallel fault-secure encoders for various systematic cyclic linear codes used in data transmission. It is assumed that the data to be encoded before transmission are stored in a fault-tolerant RAM memory system protected against errors using a cyclic linear error detecting and/or correcting code. The main idea relies on taking advantage of the RAM check bits to control the correct operation of the cyclic code encoder as well. A slightly modified encoder allows not only for encoding the transmission data stream but also, independently and in parallel, to generate the reference check bits which allow for concurrent error detection in the encoder itself. The error detection capacity proves to be effective and grants good levels of protection as shown by error injection campaigns on encoders for various standard linear cyclic error detecting and error correcting codes. Moreover, the complexity evaluation of the FPGA implementations of the encoders shows that their fault-secure versions compare favorably against the unprotected ones, both with respect to hardware complexity and the maximal frequency of operation.