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the above result by computing a basis for the Berlekamp subalgebra. This is achieved via the observation that Berlekamp subalgebra is in fact the kernel of a certain matrix over , which is derived from the so-called Berlekamp matrix of the polynomial, denoted . If then is the coefficient of the -th power term in the reduction of modulo , i.e.:

:

With a certain polynomial , say:

:

we may associate the row vector:

:

It is relatively straightforward

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