| ### C.8.3 Generalized Newton identities The error-locator polynomial is defined by 891#891 If this product is expanded, 892#892 then the coefficients 893#893 are the elementary symmetric functions in the error locations 845#845 894#894 #### Generalized Newton identities The syndromes 895#895 and the coefficients 893#893 satisfy the following generalized Newton identities: 896#896 #### Decoding up to error-correcting capacity We have 897#897, since 898#898. Furthermore 899#899 and 900#900. Replace the syndromes by variables and obtain the following set of polynomials 901#901 in the variables 902#902 and 903#903: 904#904 905#905 906#906 907#907 908#908 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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