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This paper describes a construction technique for q-ary turbo codes that computes good recursive systematic convolutional q-ary constituent codes with constraint length v/spl les/5 for q=2/sup m/, m=2, 3, and 4. The construction technique, based on the algorithm of Benedetto, Garello and Montorsi (see IEEE Trans. Commun., vol.46, p.1101-1105, 1998), determines the codes with maximum d/sub i/ for i=2, 3, and 4 and minimum codeword multiplicity, where d/sub i/ is the minimum weight of all code sequences with input weight i. Due to the large number of encoder states involved, standard weight distribution calculations are difficult. The construction algorithm employed is a computer search that generates all possible terminating sequences of weight 2, 3, and 4 to use as inputs to the set of allowable encoders.