Notes on classification of toric surface codes of dimension 5

被引：4
|
作者：
Yau, Stephen S. -T. [1 ,2 ]
Zuo, Huaiqing [3 ]
机构：
[1] Univ Illinois, Dept MSCS, Chicago, IL 60607 USA
[2] E China Normal Univ, Inst Math, Shanghai 200062, Peoples R China
[3] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
来源：
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2009年 / 20卷 / 02期
关键词：
C (programming language);
D O I：
10.1007/s00200-009-0096-2
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
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 C(P5)(7) enjoys more symmetry, and it has more codewords of minimum distance in general. However, over some special fields F(2)m, C(P5(5)) and C(P5)(7) have the same number of the codewords of minimum distance.
引用
收藏
页码：175 / 185
页数：11
相关论文
共 50 条
  • [1] Notes on classification of toric surface codes of dimension 5
    Stephen S.-T. Yau
    Huaiqing Zuo
    Applicable Algebra in Engineering, Communication and Computing, 2009, 20 : 175 - 185
  • [2] On classification of toric surface codes of low dimension
    Luo, Xue
    Yau, Stephen S-T
    Zhang, Mingyi
    Zuo, Huaiqing
    FINITE FIELDS AND THEIR APPLICATIONS, 2015, 33 : 90 - 102
  • [3] On classification of toric surface codes of dimension seven
    Hussain, Naveed
    Luo, Xue
    Yau, Stephen S-T
    Zhang, Mingyi
    Zuo, Huaiqing
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2020, 28 (02) : 263 - 319
  • [4] Classifying toric surface codes of dimension 7
    Cairncross, Emily
    Ford, Stephanie
    Garcia, Eli
    Jabbusch, Kelly
    INVOLVE, A JOURNAL OF MATHEMATICS, 2021, 14 (04): : 605 - 616
  • [5] BRINGING TORIC CODES TO THE NEXT DIMENSION
    Soprunov, Ivan
    Soprunova, Jenya
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2010, 24 (02) : 655 - 665
  • [6] Toric surface codes and Minkowski sums
    Little, John
    Schenck, Hal
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2006, 20 (04) : 999 - 1014
  • [7] Classification of Toric Surface Patches
    Sun, Lanyin
    Zhu, Chungang
    ADVANCES IN COMPUTER GRAPHICS, CGI 2023, PT III, 2024, 14497 : 174 - 185
  • [8] TORIC SURFACE CODES AND MINKOWSKI LENGTH OF POLYGONS
    Soprunov, Ivan
    Soprunova, Jenya
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2009, 23 (01) : 384 - 400
  • [9] CLASSIFICATION OF GORENSTEIN TORIC DEL PEZZO VARIETIES IN ARBITRARY DIMENSION
    Batyrev, Victor
    Juny, Dorothee
    MOSCOW MATHEMATICAL JOURNAL, 2010, 10 (02) : 285 - 316
  • [10] On the construction of Griesmer codes of dimension 5
    Yuuki Kageyama
    Tatsuya Maruta
    Designs, Codes and Cryptography, 2015, 75 : 277 - 280
12345