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For original article see G. Drolet, ibid., vol. 47, no. 9, p. 938-946, (Sept 1998). We characterize the smallest n with GF(2)[X]/(Xn + 1) containing an isomorphic copy of GF(2m). This characterization shows that the representation of finite fields described in a previous issue of the IEEE Transactions on Computers is not "optimal" as claimed. The representation considered there can often be improved significantly.