Abstract: A method and apparatus for detecting and correcting errors and erasures in product-coded data arrays by iterative syndrome processing array data in row major order and column major order. A first dense map is formed for classifying each row containing location indicia of random errors, their correction patterns, and pointers to rows containing erasure errors. This map is used to effectuate row array random error corrections in place in memory. A second dense map is formed of location indicia and correction patterns for each pair adjacent position within a column containing erasure errors as indexed by a counterpart row pointer. The second map is used to effectuate column array erasure corrections and random error corrections in place in memory.

Abstract: An apparatus and method for decoding data encoded in a linear cyclic code with less hardware than the prior art decoding apparatus without sacrificing the processing speed are described. The polynomial arithmetic part 14 derives polynomials &sgr;(x), &ohgr;(x) by repeating calculation of the following Qi(x), exchange of polynomials between the register U_reg 180 and the register X_reg 184, and exchange of polynomials between the register Y_reg 182 and the register Z_reg 186 until the degree (deg Xreg) of the polynomial in the register X_reg 184 becomes smaller than [(d−h+1)/2] to solve the following recursive formula.