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C.8.3 Generalized Newton identitiesThe error-locator polynomial is defined by
889#889
If this product is expanded,
890#890
then the coefficients 891#891 are the elementary symmetric functions in
the error locations 843#843
892#892
Generalized Newton identitiesThe syndromes 893#893 and the coefficients 891#891 satisfy the following generalized Newton identities:
894#894
Decoding up to error-correcting capacityWe have 895#895, since 896#896. Furthermore
897#897
and
898#898.
Replace the syndromes by variables and obtain the following set of polynomials 899#899 in the variables
900#900 and
901#901:
902#902
903#903
904#904
905#905
906#906
For an example see |
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