Erasure code syndrome computation based on Reed Solomon (RS) operations in a Galois field to permit reconstruction of data of more than 2 failed storage units. Syndrome computation may be performed with coefficient exponents that consist of −1, 0, and 1. A product xD of a syndrome is computed as a left-shift of data byte D, and selective compensation based on the most significant bit of D. A product x−1D of a syndrome is computed as a right-shift of data byte D, and selective compensation based on the most significant bit of D. Compensation may include bit-wise XORing shift results with a constant derived from an irreducible polynomial associated with the Galois field. A set of erasure code syndromes may be computed for each of multiple nested arrays of independent storage units. Data reconstruction includes solving coefficients of the syndromes as a Vandermonde matrix.