The extended coset leader weight enumerator of a twisted cubic code

Abstract The extended coset leader weight enumerator of the generalized Reed–Solomon $$[q+1,q-3,5]_q$$ [ q + 1 , - 3 5 ] code is computed. In this computation methods in finite geometry, combinatorics and algebraic geometry are used. For we need classification points, lines planes projective three space under projectivities that leave twisted cubic invariant. A line determines a rational function degree at most vice versa. Furthermore, double point scheme studied. pencil true passant cubic, not an osculation plane gives curve genus one as scheme. With Hasse–Weil bound on $${\mathbb F}_q$$ F -rational points show there 3-plane containing passant.