Fragments of plane filling curves of degree q + 2 over the finite field of q elements, and of affine-plane filling curves of degree q + 1.

Nonsingular plane curves over a finite field F q of degree q + 2 passing through all the F q -points of the plane admit a representation by 3 × 3 matrices over F q. We classify their degenerations by means of the matrix representation. We also discuss the similar problem for the affine-plane filling projective curves of degree q + 1. [ABSTRACT FROM AUTHOR]