On the Divisibility of Trinomials by Maximum Weight Polynomials over F2

Abstract

Divisibility of trinomials by given polynomials over finite fields has been studied and used to construct orthogonal
arrays in recent literature. Dewar et al. (Dewar et al., 2007) studied the division of trinomials by a given pentanomial
over F2 to obtain the orthogonal arrays of strength at least 3, and finalized their paper with some open questions. One
of these questions is concerned with generalizations to the polynomials with more than five terms. In this paper, we
consider the divisibility of trinomials by a given maximum weight polynomial over F2 and apply the result to the
construction of the orthogonal arrays of strength at least 3.