On classification of toric surface codes of low dimension Dedicated to Professor Ronald Graham on the occasion of his 80th birthday

Xue Luo; Stephen S.T. Yau; Mingyi Zhang; Huaiqing Zuo

doi:10.1016/j.ffa.2014.11.007

On classification of toric surface codes of low dimension Dedicated to Professor Ronald Graham on the occasion of his 80th birthday

Xue Luo
, Stephen S.T. Yau^*
, Mingyi Zhang
, Huaiqing Zuo

^*此作品的通讯作者

数学科学学院

Tsinghua University

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

This work is a natural continuation of our previous work [14]. In this paper, we give a complete classification of toric surface codes of dimension equal to 6, except a special pair, CP6₍₄₎ and CP6₍₅₎ over ^F8. Also, we give an example, CP6₍₅₎ and CP6₍₆₎ over ^F7, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.

源语言	英语
页（从-至）	90-102
页数	13
期刊	Finite Fields and their Applications
卷	33
DOI	https://doi.org/10.1016/j.ffa.2014.11.007
出版状态	已出版 - 5月 2015

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10.1016/j.ffa.2014.11.007

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abstract = "This work is a natural continuation of our previous work [14]. In this paper, we give a complete classification of toric surface codes of dimension equal to 6, except a special pair, CP6(4) and CP6(5) over F8. Also, we give an example, CP6(5) and CP6(6) over F7, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.",

keywords = "Lattice equivalence, Minimum distance, Monomially equivalent, Toric code",

author = "Xue Luo and Yau, \{Stephen S.T.\} and Mingyi Zhang and Huaiqing Zuo",

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doi = "10.1016/j.ffa.2014.11.007",

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AU - Luo, Xue

AU - Yau, Stephen S.T.

AU - Zhang, Mingyi

AU - Zuo, Huaiqing

PY - 2015/5

Y1 - 2015/5

N2 - This work is a natural continuation of our previous work [14]. In this paper, we give a complete classification of toric surface codes of dimension equal to 6, except a special pair, CP6(4) and CP6(5) over F8. Also, we give an example, CP6(5) and CP6(6) over F7, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.

AB - This work is a natural continuation of our previous work [14]. In this paper, we give a complete classification of toric surface codes of dimension equal to 6, except a special pair, CP6(4) and CP6(5) over F8. Also, we give an example, CP6(5) and CP6(6) over F7, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.

KW - Lattice equivalence

KW - Minimum distance

KW - Monomially equivalent

KW - Toric code

UR - https://www.scopus.com/pages/publications/84918555715

U2 - 10.1016/j.ffa.2014.11.007

DO - 10.1016/j.ffa.2014.11.007

M3 - 文章

AN - SCOPUS:84918555715

SN - 1071-5797

VL - 33

SP - 90

EP - 102

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

On classification of toric surface codes of low dimension Dedicated to Professor Ronald Graham on the occasion of his 80th birthday

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