Abstract
This is an addendum to the beautiful paper by Little and Schwarz (Appl Algebra Eng Commun Comput 18:349–367, 2007) in which one case of toric surface codes of dimension 5 was missing in their classification result of toric surface codes of dimension less than 6. Our main purpose is to fill the gap of this paper. We find that our new code enjoys more symmetry, and it has more codewords of minimum distance in general. However, over some special fields , and have the same number of the codewords of minimum distance.
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