This paper proposes a new test pattern generator (TPG) which is an enhancement of GLFSR (Galois LFSR). This design is based on certain non-binary error detecting codes, formulated over an extension field of GF(2δ), δ > 1. The resulting generator provides a guaranteed Hamming distance between successive test patterns, resulting in shorter test lengths. As an additional advantage, the proposed TPG has the intrinsic ability to detect 1-bit errors in the TPG itself. Detailed design methodology and experimental results are presented. The results presented here also have implications in algebraic coding theory in that they may lead to new coding techniques for test pattern generation.