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C.8.2 Cooper philosophy

Computing syndromes in cyclic code case

CRHT-ideal

Replace the concrete values above by variables and add some natural restrictions. Introduce

General error-locator polynomial

For an example see sysCRHT in decodegb_lib. More on Cooper's philosophy and the general error-locator polynomial can be found in [OS2005].

Finding the minimum distance

The method described above can be adapted to find the minimum distance of a code. More concretely, the following holds:

For an example see sysCRHTMindist in decodegb_lib. More on finding the minimum distance with Groebner bases can be found in [S2007]. See [OS2005], for the definition of the polynomial above.


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