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Abstract

Disclosed is a method and a system for error detection and correction in which codewords are made up of data and two groups of check symbols. The first group of check symbols is generated by a correction verification code, which verifies error correction; and, the second group of check symbols is generated by an interleaved Reed-Solomon code with symbols from the Galois field GF(2.sup.8), which serves for error correction. The correction verification code is cyclic with a generator polynomial g.sub.v (x)=x.sup.2 +1 over the field GF(2.sup.8). The Reed-Solomon code has a form g.sub.0 (x)=x.sup.4 +.alpha..sup.54 x.sup.3 +.alpha..sup.9 x.sup.2 +.alpha..sup.54 x+1, where .alpha. is a primitive element of the field GF(2.sup.8), generated by a polynomial p(x)=x.sup.8 +x.sup.6 +x.sup.5 +.sup.4 +1. The error correction system decoder uses the first root x.sub.1 of an error location polynomial .sigma.(x)=x.sup.2 +.sigma..sub.1 x+.sigma..sub.2 to calculate the second root x.sub.2 of the polynominal. The detection system, which employs a portion of the error correction system circuitry, uses a generalized Hamming cyclic code with a generator polynomial g.sub.d (x)=x.sup.2 +.alpha..sup.9 x+1 where .alpha. is a root of a primitive polynomial p(x)=x.sup.8 +x.sup.6 +x.sup.5 +x.sup.4 +1 over the field GF(2).

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First Claim