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arXiv · 1910.02648

A note on hyperquadratic elements of low algebraic degree

Alain Lasjaunias
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Abstract

In different areas of discrete mathematics, a certain type of polynomials, having coefficients in a field K of finite characteristic, has been considered. The form and the degree of these polynomials, here called projective, are simply linked to the characteristic p of K. Roots of these projective polynomials are particular algebraic elements over K, called hyperquadratic. For a general algebraic element of degree d over K, we discuss the possibility of being hyperquadratic. Using a method of differential algebra, we obtain, for particular fields K = Fp, projective polynomials only having polynomial factors of degree 1 or 2.

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Alain Lasjaunias. 2019-10-07. A note on hyperquadratic elements of low algebraic degree. https://arxiv.org/abs/1910.02648

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