Journal of Beijing University of Posts and Telecommunications

  • EI核心期刊

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2004, Vol. 27 ›› Issue (5): 21-25.

• PAPERS • Previous Articles     Next Articles

Weight Hierarchies of Linear Codes Satisfying the Break-Chain Condition

WANG Yong-hui, CHEN Wen-de   

  1. Laboratory of Systems and Control and Information Security Center, Academy of Mathematics
    and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2003-11-22 Online:2004-05-28

Abstract: The weight hierarchy of a linear [n,k;q] codeC over GF(q) is the sequece (d1, d2, … dk), where dr isthe smallest support weight of an r-dimensional subcode of C. The weight hierarchies of linear codes satisfying the break-chain condition containing many abutal break points of general dimension over GF(q) are investigated. First,a simple necessary condition for a sequence to be the weight hierarchies of suchcodes are given. Further, by using the finite projective geometry method, explicit constructions of such codes are given, showing that in almost all cases, thenecessary conditions are also sufficient by properly choosing the subspaces inthe projective space. And so, almost all the weight hierarchies of such codes are determined.

Key words: weight hierarchy, deference sequence, break-chain condition.

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