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

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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).

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Authors and Affiliations

  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

    Wen De Chen

  2. Department of Informatics, University of Bergen, Bergen High Technology Center, N-5020, Bergen, Norway

    Torleiv Kløve

Authors
  1. Wen De Chen
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  2. Torleiv Kløve
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Correspondence to Wen De Chen.

Additional information

The research is supported by The Norwegian Research Council and the National Science Foundation of China (10271116)

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Chen, W.D., Kløve, T. Finite Projective Geometries and Classification of the Weight Hierarchies of Codes (I). Acta Math Sinica 20, 333–348 (2004). https://doi.org/10.1007/s10114-004-0337-z

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  • DOI: https://doi.org/10.1007/s10114-004-0337-z

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