An error detection module includes a known-syndrome computing unit, an unknown-syndrome computing unit, and an error detection unit. The known-syndrome computing unit is operable to convert a received signal into a target signal, to obtain known syndromes based upon the target signal, and to generate an errata-locator polynomial based upon an erasure-locator polynomial and the known syndromes. The unknown-syndrome computing unit is operable to compute unknown syndromes based upon the errata-locator polynomial and the known syndromes. The error detection unit is operable to obtain a syndrome set that includes the known syndromes and the unknown syndromes, to obtain an error detection signal according to the syndrome set, and to provide an error correction module coupled thereto with the syndrome set and the error detection signal for enabling the error correction module to correct an error of the received signal.