On classification of toric surface codes of low dimension

This work is a natural continuation of our previous work [14]. In this paper, we give a complete classification of toric surface codes of dimension equal to 6, except a special pair, CP6(4) and CP6(5) over F8. Also, we give an example, CP6(5) and CP6(6) over F7, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.