1. A decoder apparatus responsive to a received data vector having a plurality of symbols and being based on a predetermined encoding polynomial, comprising: first processing means responsive to the received data vector for iteratively calculating intermediate components of a time domain syndrome vector, and for calculating locations and counts of erasures in the received data vector, and further for iteratively extending the time domain syndrome vector in response to a discrepancy constant to provide an extended syndrome vector, wherein the final extended syndrome vector represents an error vector; second processing means responsive to the extended time domain syndrome vector components, to intermediate components of an errata vector, and to the erasure locations and counts for iteratively calculating components of the errata vector and for storing said iteratively calculated components of the errata vector, and further for calculating a discrepancy constant based on each iteration of said intermediate extended syndrome vector components and said errata vector components; third processing means, responsive to the erasure locations and counts, for iteratively calculating intermediate components of an erasure vector and for storing said intermediate erasure vector components, and responsive to the erasure vector components and the erasure locations and counts, for iteratively calculating said intermediate errata vector components, and responsive to the received data vector and the error vector for providing a corrected output signal; and control means for controlling the operations of said first, second, and third processing means.