Maximal arcs and extended cyclic codes

Abstract

It is proved that for every $$d\ge 2$$ such that $$d-1$$ divides $$q-1$$ , where q is a power of 2, there exists a Denniston maximal arc A of degree d in $${\mathrm {PG}}(2,q)$$ , being invariant under a cyclic linear group that fixes one point of A and acts regularly on the set of the remaining points of A. Two alternative proofs are given, one geometric proof based on Abatangelo–Larato’s characterization of Denniston arcs, and a second coding-theoretical proof based on cyclotomy and the link between maximal arcs and two-weight codes.