A single polynomial expander 22 is time multiplexed to produce firstly a modified syndrome polynomial T(x) and then an erasure located polynomial .LAMBDA.(x). T(x) is supplied to a key equation solving unit 32 which solves the key equation to calculate an error locator polynomial .sigma.(x) and an errata evaluator polynomial .omega.(x). These polynomials .sigma.(x), .LAMBDA.(x) and .omega.(x) form three inputs to polynomial evaluators 52 56 and a Forney block 62 for determining the location and magnitude of each symbol error and symbol erasure, allowing the received codeword to be corrected in a correction block 72. Optionally, a transform block 42 is provided to avoid unnecessary delay and improve throughput when decoding shortened codewords.