On Classification of Toric Surface Codes of Low Dimension

Abstract

This work is a natural continuation of our previous work \cite{yz}. In this paper, we give a complete classification of toric surface codes of dimension less than or equal to 6, except a special pair, $C_{P_6^{(4)}}$ and $C_{P_6^{(5)}}$ over ${\mathbb{F}}_8$. Also, we give an example, $C_{P_6^{(5)}}$ and $C_{P_6^{(6)}}$ over ${\mathbb{F}}_7$, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.

18 pages, 4 figures, 8 tables

Cited by in corpus (1)

• Classifying toric surface codes of dimension $7$