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On Classification of Toric Surface Codes of Low Dimension (1402.0060v2)
Published 1 Feb 2014 in cs.IT, math.CO, and math.IT
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.