2024/02/22 by Valentino Smaldore, Corrado Zanella, Smaldore, Valentino +3 · 2 citations
Mathematics · Engineering · #Mathematics and Applications #Advanced Numerical Analysis Techniques #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2402.14742
Let 18 only three families of scattered polynomials in \mathbb Fqn[X] are known: (i)~monomials of pseudoregulus type, (ii)~binomials of Lunardon-Polverino type, and (iii)~a family of quadrinomials defined in [1,10] and extended in [8,13]. In this paper we prove that the polynomial φm,qJ=X^qJ(t-1)+X^qJ(2t-1)+m(XqJ-X^qJ(t+1))∈\mathbb Fq2t[X], q odd, t≥3 is R-qt-partially scattered for every value of m∈\mathbb Fqt^* and J coprime with 2t. Moreover, for every t>4 and q>5 there exist values of m for which φm,q is scattered and new with respect to the polynomials mentioned in (i), (ii) and (iii) above. The related linear sets are of ΓL-class at least two.