The weight distributions of linear sets in PG(1,q⁵)

Authors

Maarten De Boeck, Faculty of Mathematics, University of Rijeka
Geertrui Van de Voorde, University of Canterbury

Abstract

In this paper, we study the weight distributions of Fq-linear sets in PG(1,q5). Our Main Theorem proves that a linear set S of rank 5, which is not scattered has the following weight distribution for its points with weight larger than 1: (i) one point of weight 4 or 5, (ii) one point of weight 3 and 0, q, or q2 points of weight 2, (iii) s points of weight 2 where s∈[q−2q+1,q+2q+1]∪{2q,2q+1,2q+2,3q,3q+1,q2+1}. In particular, there are no 2-clubs in PG(1,q5).

Publication Title

Finite Fields and their Applications

Recommended Citation

De Boeck, M., & Van de Voorde, G. (2022). The weight distributions of linear sets in PG(1,q⁵). Finite Fields and their Applications, 82 https://doi.org/10.1016/j.ffa.2022.102034