| ### C.8.3 Generalized Newton identities The error-locator polynomial is defined by If this product is expanded, then the coefficients are the elementary symmetric functions in the error locations #### Generalized Newton identities The syndromes and the coefficients satisfy the following generalized Newton identities: #### Decoding up to error-correcting capacity We have , since . Furthermore and . Replace the syndromes by variables and obtain the following set of polynomials in the variables and : 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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