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On classification of toric surface codes of dimension seven

NAVEED HUSSAIN, xue Luo stephen S.-T. YAU Tsinghua University MINGYI ZHANG Huaiqing Zuo Tsinghua university

Information Theory mathscidoc:1803.19001

to appear Comm. Anal. Geometry, 2018
In this paper, we give an almost complete classi cation of toric surface codes of dimension less than or equal to 7, according to monomially equivalence. This is a natural extension of our previous work [YZ], [LYZZ]. More pairs of monomially equivalent toric codes constructed from non-equivalent lattice polytopes are discovered. A new phenomenon appears, that is, the monomially non-equivalence of two toric codes C P(10)7and CP(19)7 can be discerned on Fq, for all q  8, except q = 29. This sudden break seems to be strange and interesting. Moreover, the parameters, such as the numbers of codewords with di erent weights, depends on q heavily. More meticulous analyses have been made to have the possible distinct families of reducible polynomials.
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@inproceedings{naveed2018on,
  title={ON CLASSIFICATION OF TORIC SURFACE CODES OF DIMENSION SEVEN},
  author={NAVEED HUSSAIN,, xue Luo, stephen  S.-T. YAU, MINGYI ZHANG, and Huaiqing Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180307151659174572978},
  booktitle={to appear Comm. Anal. Geometry},
  year={2018},
}
NAVEED HUSSAIN,, xue Luo, stephen S.-T. YAU, MINGYI ZHANG, and Huaiqing Zuo. ON CLASSIFICATION OF TORIC SURFACE CODES OF DIMENSION SEVEN. 2018. In to appear Comm. Anal. Geometry. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180307151659174572978.
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