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Cellular automata-based bit error correcting codes over binary field was originally studied by Chowdhury et al. (IEEE Trans. Comput. 43:759-764, ) 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. [ABSTRACT FROM AUTHOR]

In this paper, we obtain bounds for error correcting codes of some particular homogeneous weights over the ring of integers modulo $${2^l( {l\ge 3})}$$. We also study these bounds to check for perfect linear codes and have shown the non-existence of one error correcting perfect codes with respect to the homogeneous weight. [ABSTRACT FROM AUTHOR]