Efficient error bit identification from failing signatures

Efficient identification of bit errors in the input to single and multiple input signature registers is obtained using a characteristic polynomial constructed from the product of multiple polynomials. This set of multiple polynomials may be primitive and/or non-primitive but must have different orders. The degree of the input polynomial to the signature register is limited to the least common multiple of the orders of these polynomials. The identification algorithm is based on look-up tables with the total number of entries equal the sum of the orders of these polynomials, making the technique more efficient than previous approaches in terms of both hardware and algorithmic complexity.