Summary: It is shown that soft decision maximum likelihood decoding of any \((n,k)\) linear block code over \(\mathrm{GF}(q)\) can be accomplished using the Viterbi algorithm applied to a trellis with no more than \(q^{(n-k)}\) states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer than \(q^{n-k}\). For a binary \((n,n - 1)\) single parity check code, the Viterbi algorithm is equivalent to the Wagner decoding algorithm.