Two pointsets in \(\mathrm{PG}(2,q^n)\) and the associated codes (Q6112231)

The authors' aim is to construct codes with few weights arising from linear sets in a projective line. To this end, they start with a linear set \(L\) of rank \(n\) contained in a line of \(\mathrm{PG}(2, q^n)\) and construct two point sets of \(\mathrm{PG}(2,q^n)\) associated with \(L\). They show that the pattern of intersection of their two point sets with lines of \(\mathrm{PG}(2,q^n)\) is strongly related to the weight distribution of the linear set \(L\). This allows them to construct a large number of linear codes for which they can completely describe the weight distribution, thereby obtaining some linear codes with few weights.