Cellular automata-based bit error correcting codes over binary field was originally studied by Chowdhury et al. (IEEE Trans. Comput. 43:759-764, 1994) and also an algorithm for decoding such codes was introduced. Further, for the binary field case, it was shown that cellular automata-based error correcting codes have faster decoding algorithm than the classical linear syndrome decoding algorithm. We generalize Chowdhury's approach from binary to primitive finite fields and we also compare the classical syndrome decoding with the one introduced in this work. We show that error correcting codes obtained via cellular automata have faster decoding than the classical ones.