Notes on classification of toric surface codes of dimension 5
Notes on classification of toric surface codes of dimension 5
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DOI：
10.1007/s00200-009-0096-2
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
S. Yau;Huaiqing Zuo
中科院分区：
文献类型：
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作者：
S. Yau;Huaiqing Zuo
这是 Little 和 Schwarz 的精彩论文的附录（Appl Algebra Eng Commun Comput 18:349–367, 2007），其中在对维度小于 6 的复曲面代码的分类结果中缺少一个维度 5 的复曲面代码的情况。我们的主要目的是填补本文的空白。我们发现我们的新代码具有更多的对称性，并且总体上具有更多的最小距离码字。然而，在一些特殊领域，最小距离的码字数量相同。
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 codeenjoys more symmetry, and it has more codewords of minimum distance in general. However, over some special fields,andhave the same number of the codewords of minimum distance.