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C.8.3 Generalized Newton identitiesThe 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 identitiesThe syndromes 895#895 and the coefficients 893#893 satisfy the following generalized Newton identities:
896#896
Decoding up to error-correcting capacityWe 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 |
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