An encoded message is stored in a first memory. The encoded message is retrieved from the first memory as a retrieved encoded message that may contain an error. Syndromes are generated from the retrieved encoded message. The syndromes are used to determine if the retrieved encoded message has an error. Polynomial coefficients are generated for establishing a polynomial equation having a first number of solutions. The polynomial equation is solved only for a second number of solutions. The first number is greater than the second number. The second number of solutions comprises solutions corresponding to locations in the retrieved encoded message. Each location is corrected in the retrieved encoded message that corresponds to a solution of zero of the polynomial equation. The result is efficient error correction.