Finite Projective Geometries and Classification of the Weight Hierarchies of Codes (I)

Authors
Chen, Wen Chen Kløve, Torleiv
Citation
Chen, Wen Chen et Kløve, Torleiv, Finite Projective Geometries and Classification of the Weight Hierarchies of Codes (I), Acta mathematica Sinica. English series (Print) , 20(2), 2004, pp. 333-348
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
20
Issue
2
Year of publication
2004
Pages
333 - 348
Database
ACNP
SICI code
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).