Error correction method including erasure correction, and apparatus

Abstract

A multiplier calculates a product S'(x)=S(x).multidot..lambda.(x) mod X.sup.d-1 of a syndrome polynomial S(x) generated by a syndrome generator and an erasure position polynomial .lambda.(x) generated by an erasure position polynomial generator, modulo X.sup.d-1. A constant multiplier sequentially multiplies coefficients of the polynomial S'(x) and the erasure position polynomial .lambda.(x) with a power of a primitive root .alpha. of a code. The power exponents in this multiplication are determined in units of coefficients. Every time this multiplication is executed, an adder sequentially adds predetermined combinations of products. A plurality of arithmetic and logic operations according to the numbers of correctable erasures and errors are sequentially executed using the sums. A divisor and dividend are selected in accordance with the number of erasures included in the code on the basis of the plurality of arithmetic and logic operation results. A division is executed using the selected divisor and dividend. A value at a position, discriminated to be an error position, of the code is corrected based on the division result, thus performing error correction including erasure correction with a simple circuit arrangement.