The number of solutions of an equation related to a product of multilinear polynomials

Details The number of solutions of an equation related to a product of multilinear polynomials The number of solutions of an equation related to a product of multilinear polynomials

2006-03-02

arxiv.org/abs/math/0603057v1

Mathematics

Number Theory

17 pages

Scientific paper

We look at the number of solutions of an equation of the form f_1*f_2*...*f_k=a in a finite field, where each f_i is a multilinear polynomial. We use two methods to construct a solution of this problem for the cases a=0, a<>0, and we generally get a semi-explicit formula. We show that this formula can generate a more efficient algorithm than the traditional algorithm which consists to make a systematic computation. We also give explicit formulas in some special cases, and an application of our main result to the search of the weight hierarchy of the multilinear code with separated variables.

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