In this paper, we present a lower bound for the dimension of subfield subcodes of residue Goppa codes on the curve Cab, which exceeds the lower bound given by Stichtenoth when the number of check symbols is not small. We also give an illustrative example which shows that the proposed bound for the dimension of certain residue Goppa code exceeds the true dimension of a BCH code with the same code length and designed distance.

In this paper, we show that the conventional BCH codes can be better than the AG codes when the number of check symbols is relatively small. More precisely, we consider an AG code on Cab whose number of check symbols is less than min {g+a, n-g}, where n and g denote the code length and the genus of the curve, respectively. It is shown that there always exists an extended BCH code, (i) which has the same designed distance as the Feng-Rao designed distance of the AG code and the code length and the rate greater than those of the AG code, or (ii) which has the same number of check symbols as that of the AG code, the designed distance not less than that of the AG code and the code length longer than that of the AG code.