A method for decoding an Error Correction Code (ECC) includes accepting coefficients, including at least first and second coefficients, of an Error Locator Polynomial (ELP) that is defined over a vector space and has at least one root that is indicative of a location of an error in a set of bits, which represent data that has been encoded with the ECC. The first coefficient is represented using a first basis of the vector space, and the second coefficient is represented using a second basis of the vector space, different from the first basis. Using processing circuitry, the root of the ELP is identified by applying algebraic operations to the coefficients, such that the algebraic operations are applied to the first coefficient using the first basis, and to the second coefficient using the second basis. The error is corrected responsively to the identified root of the ELP.