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This paper presents a method to protect memories against multiple bit upsets and to improve manufacturing yield. The proposed method, called a Matrix code, combines Hamming and Parity codes to assure the improvement of reliability and yield of the memory chips in the presence of high defects and multiple bit-upsets. The method is evaluated using fault injection experiments. The results are compared to well-known techniques such as Reed-Muller and Hamming codes. The proposed technique performs better than the Hamming codes and achieves comparable performance with Reed-Muller codes with very favorable implementation gains such as 25% reduction in area and power consumption. It also achieves reliability increase by more than 50% in some cases. Further, the yield benefits provided by the proposed method, measured by the yield improvements per cost metric, is up to 300% better than the ones provided by Reed-Muller codes.