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Convolutional doubly orthogonal (CDO) codes constitute a recent group of binary error correcting codes for additive white gaussian noise channel, achieving very good error performance at moderate values of Eb/N0 under the threshold decoding algorithm. Inspired by the low-density parity-check codes over the finite fields, this study extends the construction and decoding of single shift register CDO codes from binary field to the finite fields GF(q) for q > 2, referred to as the q-ary CDO codes. The threshold decoding algorithm is modified to accommodate the decoding requirement for this set of codes. Superior error performance has been observed for q-ary CDO codes over their binary counterparts, especially in the error floor region.