An algebraic complete decoding for double-error-correcting binary BCH codes
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An algebraic complete decoding for double-error-correcting binary BCH codes of primitive length is derived. The decoding is done more quickly than the step-by-step decoding devised by Hartmann. And if an error pattern corresponding with syndromess 1 ands 2 has weight 3, the decoding can find all error patterns of weight 3 corresponding with these syndromes. At the same time, a discriminant for a polynomial of degree 3 overGF(2 m ) has three distinct roots inGF2 m ) is also derived. The discriminant is very important for complete decoding of triple-error-correcting binary BCH codes.
KeywordsConjugate Class Minimum Polynomial Error Pattern Primitive Element Distinct Root
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