Error correction method and apparatus thereof

An error correction apparatus for correcting errors in received digital data signals, comprising:

• a syndrome calculator for calculating syndromes S.sub.0, S.sub.1, S.sub.2, and S.sub.3 from n received digital data words;
• a first coefficient calculator for calculating coefficients .sigma..sub.1 and .sigma..sub.2 from said syndromes according to the equations:
• ##EQU39## a second coefficient calculator for calculating a coefficient K from said coefficients .sigma..sub.1 and .sigma..sub.2 according to the equation:
• ##EQU40## where K GF (2.sup.8);
• an x.sub.1 value calculator for calculating a value x.sub.1 from the coefficient K;
• an error location value calculator for calculating the following error locations X.sub.1 and X.sub.2 from said value x.sub.1
• X.sub.1 =x.sub.1 .sigma..sub.1
• X.sub.2 =(1+x.sub.1).sigma..sub.1
• an error value calculator for receiving said error location values X.sub.1 and X.sub.2 and then calculating the following error values Y.sub.1 and Y.sub.2 ##EQU41## an error discriminator for determining how many errors exist in said received digital data;
• and
• an error corrector for correcting said determined errors by adding said error values Y.sub.1 and Y.sub.2 to said received digital data words;
• wherein the x.sub.1 value calculator uses XOR logic gates which satisfy the following equations:
• X.sub.0 =k.sub.3 +k.sub.5 +k.sub.6
• X.sub.1 =k.sub.0 +k.sub.2 +k.sub.4
• X.sub.2 =k.sub.0 +k.sub.3 +k.sub.4 +k.sub.6
• X.sub.3 =k.sub.1 +k.sub.2 +k.sub.3 +k.sub.4
• X.sub.4 =k.sub.0 +k.sub.7
• X.sub.5 =k.sub.1 +k.sub.2 +k.sub.3 +k.sub.4 +k.sub.6
• X.sub.6 =k.sub.0 +k.sub.1 +k.sub.2 +k.sub.4 +k.sub.7
• X.sub.7 =k.sub.0 +k.sub.1 +k.sub.2 +k.sub.4
• in which x.sub.1 =[X.sub.0, X.sub.1, X.sub.2, . . . , X.sub.7 ].