 Consequently a polynomial formula_10 is in the Berlekamp subalgebra if and only if formula_34 (where formula_35 is the formula_18 identity matrix), i.e.if and only if it is in the null space of formula_37.By computing the matrix formula_37 and reducing it to reduced row echelon form and then easily reading off a basis for the null space, we may find a basis for the Berlekamp subalgebra and hence construct polynomials formula_4 in it.