| Finite Projective Geometries and Classification of the Weight Hierarchies of Codes （Ⅰ） |
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| 引用本文： | WenDeCHEN TorleivKLφVE.Finite Projective Geometries and Classification of the Weight Hierarchies of Codes （Ⅰ）[J].数学学报(英文版),2004,20(2):333-348. |
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| 作者姓名： | WenDeCHEN TorleivKLφVE |
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| 作者单位： | [1]LaboratoryofSystemsandControl,CenterofInformationSecurity,AcademyofMathematicsandSystemsScience,ChineseAcademyofSciences,Beijing100080,P.R.China [2]Departmentoflnformatics,UniversityofBergen,BergenHighTechnologyCenter,N-5020Bergen,Norway |
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| 摘 要： | The weight hierarchy of a binary linear n,κ] code C is the sequence (d1,d2,...,dκ), where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries.The possible weight hierarchies in class A, B, C, D are determined in Part (Ⅰ). The possible weight hierarchies in class E, F, G, H, I are determined in Part (Ⅱ).
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| 关 键 词： | 重力层次 有限射影几何 二元线性编码 限定条件 可微序列 |
| 收稿时间： | 3 July 2000 |
Finite Projective Geometries and
Classification of the Weight Hierarchies of Codes
(I) |
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| Wen?De?ChenEmail author,Torleiv?Kl?ve.Finite Projective Geometries and
Classification of the Weight Hierarchies of Codes
(I)[J].Acta Mathematica Sinica,2004,20(2):333-348. |
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| Authors: | Email author" target="_blank">Wen?De?ChenEmail author Torleiv?Kl?ve |
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| Institution: | (1) Laboratory of Systems and Control, Center of Information Security, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China;(2) Department of Informatics, University of Bergen, Bergen High Technology Center, N-5020 Bergen, Norway |
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| Abstract: | Abstract
The weight hierarchy of a binary linear n, k] code C is the sequence (d
1,
d
2, .
. . , d
k
), where
d
r
is the smallest support
of an r-dimensional subcode
of C. The codes of dimension
4 are collected in classes and the possible weight hierarchies
in each class is determined by finite projective geometries. The
possible weight hierarchies in class A, B, C, D are determined
in Part (I). The possible weight hierarchies in class E, F, G,
H, I are determined in Part (II).
The research is supported by The Norwegian Research
Council and the National Science Foundation of China
(10271116) |
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| Keywords: | Weight hierarchy Support weight Finite projective geometries Binary linear code Chain condition Difference sequence |
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