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C.8.3 Generalized Newton identities

The 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 identities

The syndromes 893#893 and the coefficients 891#891 satisfy the following generalized Newton identities:

894#894

Decoding up to error-correcting capacity

We 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 sysNewton in decodegb_lib. More on this method and the method based on Waring function can be found in [ABF2002]. See also [ABF2008].


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