| ### 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].

User manual for Singular version 4.4.0, 2024, generated by texi2html.